CALCULUS EARLY TRANSCENDENTALS W/ WILE
CALCULUS EARLY TRANSCENDENTALS W/ WILE
11th Edition
ISBN: 9781119228509
Author: Anton
Publisher: WILEY
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Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
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Chapter 4.4, Problem 30ES

Use a graphing utility to estimate the absolute maximum and minimum values of f , if any, on the stated interval, and then use calculus methods to find the exact values.

f x = x − 1 2 x + 2 2 ;     − ∞ ,   + ∞

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(b) Find the (instantaneous) rate of change of y at x = 5. In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the following limit. lim h→0 - f(x + h) − f(x) h The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule defining f. f(x + h) = (x + h)² - 5(x+ h) = 2xh+h2_ x² + 2xh + h² 5✔ - 5 )x - 5h Step 4 - The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x). - f(x + h) f(x) = = (x² x² + 2xh + h² - ])- = 2x + h² - 5h ])x-5h) - (x² - 5x) = ]) (2x + h - 5) Macbook Pro
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Let f be defined as follows. y = f(x) = x² - 5x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 4 to x = 5 from x = 4 to x = 4.5 from x = 4 to x = 4.1 (b) Find the (instantaneous) rate of change of y at x = 4. Need Help? Read It Master It

Chapter 4 Solutions

CALCULUS EARLY TRANSCENDENTALS W/ WILE

Ch. 4.1 - (a) A function f is increasing on a,b if whenever...Ch. 4.1 - Let fx=0.1x33x29x . Then...Ch. 4.1 - Suppose that fx has derivative fx=x42ex/2 . Then...Ch. 4.1 - Consider the statement “The rise in the cost of...Ch. 4.1 - In each part, sketch the graph of a function f...Ch. 4.1 - In each part, sketch the graph of a function f...Ch. 4.1 - Use the graph of the equation y=fx in the...Ch. 4.1 - Use the graph of the equation y=fx in the...Ch. 4.1 - Use the graph of y=fx in the accompanying figure...Ch. 4.1 - Use the graph of y=fx in the accompanying figure...
Ch. 4.1 - In each part, use the graph of y=fx in the...Ch. 4.1 - Prob. 8ESCh. 4.1 - A sign chart is presented for the first and second...Ch. 4.1 - A sign chart is presented for the first and second...Ch. 4.1 - Assume that f is differentiable everywhere....Ch. 4.1 - Assume that f is differentiable everywhere....Ch. 4.1 - Assume that f is differentiable everywhere....Ch. 4.1 - Assume that f is differentiable everywhere....Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Find: (a) the intervals on which f is increasing,...Ch. 4.1 - Analyze the trigonometric function f over the...Ch. 4.1 - Analyze the trigonometric function f over the...Ch. 4.1 - Analyze the trigonometric function f over the...Ch. 4.1 - Analyze the trigonometric function f over the...Ch. 4.1 - Analyze the trigonometric function f over the...Ch. 4.1 - Analyze the trigonometric function f over the...Ch. 4.1 - In parts (a)-(c), sketch a continuous curve y=fx...Ch. 4.1 - In each part sketch a continuous curve y=fx with...Ch. 4.1 - If f is increasing on an interval 0,b, then it...Ch. 4.1 - If f is increasing on an interval 0,b, then it...Ch. 4.1 - If f is increasing on an interval 0,b, then it...Ch. 4.1 - If f is increasing on an interval 0,b, then it...Ch. 4.1 - If f is increasing on an interval 0,b, then it...Ch. 4.1 - If f is increasing on an interval 0,b, then it...Ch. 4.1 - Use a graphing utility to generate the graphs of f...Ch. 4.1 - Use a graphing utility to generate the graphs of f...Ch. 4.1 - Use a CAS to find f and to approximate the...Ch. 4.1 - Use a CAS to find f and to approximate the...Ch. 4.1 - Use Definition to prove that is increasing on . Ch. 4.1 - Use Definition to prove that is increasing on . Ch. 4.1 - Determine whether the statements are true or...Ch. 4.1 - Determine whether the statements are true or...Ch. 4.1 - In each part, find functions f and g that are...Ch. 4.1 - In each part, find functions f and g that are...Ch. 4.1 - (a) Prove that a general cubic polynomial (b)...Ch. 4.1 - From Exercise 57, the polynomial fx=x3+bx2+1 has...Ch. 4.1 - Use Definition 4.1.1 to prove: (a) If f is...Ch. 4.1 - Use part (a) of Exercise 59 to show that fx=x+sinx...Ch. 4.1 - Use part (b) of Exercise 59 to show that fx=cosxx...Ch. 4.1 - Let y=1/1+x2 . Find the value of x for which y is...Ch. 4.1 - Prob. 63ESCh. 4.1 - Prob. 64ESCh. 4.1 - Prob. 65ESCh. 4.1 - Prob. 66ESCh. 4.1 - Suppose that a population y grows according to the...Ch. 4.1 - Suppose that the number of individuals at time t...Ch. 4.1 - Suppose that the spread of a flu virus on a...Ch. 4.1 - The logistic growth model given in Formula (1) is...Ch. 4.1 - Assuming that and are positive constants, verify...Ch. 4.1 - Explain what the sign analyses of and tell us...Ch. 4.2 - A function f has a relative maximum at x0 if there...Ch. 4.2 - Suppose that f is defined everywhere and x=2,3,5,7...Ch. 4.2 - Suppose that f id defined everywhere and x=2 and...Ch. 4.2 - Let fx=x242 . Then fx=4xx24 and fx=43x24 ....Ch. 4.2 - In each part, sketch the graph of a continuous...Ch. 4.2 - In each part, sketch the graph of a continuous...Ch. 4.2 - (a) Use both the first and second derivative tests...Ch. 4.2 - (a) Use both the first and second derivative tests...Ch. 4.2 - (a) Show that both of the functions fx=x14 and...Ch. 4.2 - (a) Show that fx=1x5 and gx=3x48x3 both have...Ch. 4.2 - Locate the critical points and identify which...Ch. 4.2 - Locate the critical points and identify which...Ch. 4.2 - Locate the critical points and identify which...Ch. 4.2 - Locate the critical points and identify which...Ch. 4.2 - Locate the critical points and identify which...Ch. 4.2 - Locate the critical points and identify which...Ch. 4.2 - Locate the critical points and identify which...Ch. 4.2 - Locate the critical points and identify which...Ch. 4.2 - Assume that is continuous everywhere. Determine...Ch. 4.2 - Assume that f is continuous everywhere. Determine...Ch. 4.2 - Assume that f is continuous everywhere. Determine...Ch. 4.2 - Assume that f is continuous everywhere. Determine...Ch. 4.2 - The graph of a function fx is given. Sketch graphs...Ch. 4.2 - The graph of a function fx is given. Sketch graphs...Ch. 4.2 - Use the graph of f shown in the figure to estimate...Ch. 4.2 - Use the graph of f shown in the figure to estimate...Ch. 4.2 - Use the graph of f shown in the figure to estimate...Ch. 4.2 - Use the graph of f shown in the figure to estimate...Ch. 4.2 - Use the given derivative to find all critical...Ch. 4.2 - Use the given derivative to find all critical...Ch. 4.2 - Use the given derivative to find all critical...Ch. 4.2 - Use the given derivative to find all critical...Ch. 4.2 - Use the given derivative to find all critical...Ch. 4.2 - Use the given derivative to find all critical...Ch. 4.2 - Use the given derivative to find all critical...Ch. 4.2 - Use the given derivative to find all critical...Ch. 4.2 - Find the relative extrema using both first and...Ch. 4.2 - Find the relative extrema using both first and...Ch. 4.2 - Find the relative extrema using both first and...Ch. 4.2 - Find the relative extrema using both first and...Ch. 4.2 - Use any method to find the relative extrema of the...Ch. 4.2 - Use any method to find the relative extrema of the...Ch. 4.2 - Use any method to find the relative extrema of the...Ch. 4.2 - Use any method to find the relative extrema of the...Ch. 4.2 - Use any method to find the relative extrema of the...Ch. 4.2 - Use any method to find the relative extrema of the...Ch. 4.2 - Use any method to find the relative extrema of the...Ch. 4.2 - Use any method to find the relative extrema of the...Ch. 4.2 - Use any method to find the relative extrema of the...Ch. 4.2 - Use any method to find the relative extrema of the...Ch. 4.2 - Use any method to find the relative extrema of the...Ch. 4.2 - Use any method to find the relative extrema of the...Ch. 4.2 - Use any method to find the relative extrema of the...Ch. 4.2 - Use any method to find the relative extrema of the...Ch. 4.2 - Give a graph of the polynomial and label the...Ch. 4.2 - Give a graph of the polynomial and label the...Ch. 4.2 - Give a graph of the polynomial and label the...Ch. 4.2 - Give a graph of the polynomial and label the...Ch. 4.2 - Give a graph of the polynomial and label the...Ch. 4.2 - Give a graph of the polynomial and label the...Ch. 4.2 - Give a graph of the polynomial and label the...Ch. 4.2 - Give a graph of the polynomial and label the...Ch. 4.2 - Give a graph of the polynomial and label the...Ch. 4.2 - Give a graph of the polynomial and label the...Ch. 4.2 - In each part: (i) Make a conjecture about the...Ch. 4.2 - Sketch the graph of y=xamxbn for the stated values...Ch. 4.2 - Find the relative extrema in the interval 0x2, and...Ch. 4.2 - Find the relative extrema in the interval 0x2, and...Ch. 4.2 - Find the relative extrema in the interval 0x2, and...Ch. 4.2 - Find the relative extrema in the interval 0x2, and...Ch. 4.2 - Use a graphing utility to make a conjecture about...Ch. 4.2 - Use a graphing utility to make a conjecture about...Ch. 4.2 - Use a graphing utility to make a conjecture about...Ch. 4.2 - Use a graphing utility to make a conjecture about...Ch. 4.2 - Use a graphing utility to generate the graphs of f...Ch. 4.2 - Use a graphing utility to generate the graphs of f...Ch. 4.2 - Use a CAS to graph f and f, and then use those...Ch. 4.2 - Use a CAS to graph f and f, and then use those...Ch. 4.2 - Use a CAS to graph f and f, and then use those...Ch. 4.2 - Use a CAS to graph f and f, and then use those...Ch. 4.2 - In each part, find k so that f has a relative...Ch. 4.2 - (a) Use a CAS to graph the function fx=x4+1x2+1...Ch. 4.2 - Function similar to fx=12ex2/2 arise in a wide...Ch. 4.2 - Functions of the form fx=xnexn!,x0 where n is a...Ch. 4.2 - Let h and g have relative maxima at x0 . Prove or...Ch. 4.3 - Let fx=3x+1x3x+2x4 . Given that...Ch. 4.3 - Let fx=x24x8/3 . Given that...Ch. 4.3 - Let fx=x22ex/2 . Given that...Ch. 4.3 - Give a graph of the rational function and label...Ch. 4.3 - Give a graph of the rational function and label...Ch. 4.3 - Give a graph of the rational function and label...Ch. 4.3 - Give a graph of the rational function and label...Ch. 4.3 - Give a graph of the rational function and label...Ch. 4.3 - Give a graph of the rational function and label...Ch. 4.3 - Give a graph of the rational function and label...Ch. 4.3 - Give a graph of the rational function and label...Ch. 4.3 - Give a graph of the rational function and label...Ch. 4.3 - Give a graph of the rational function and label...Ch. 4.3 - Give a graph of the rational function and label...Ch. 4.3 - Give a graph of the rational function and label...Ch. 4.3 - Give a graph of the rational function and label...Ch. 4.3 - Give a graph of the rational function and label...Ch. 4.3 - In each part, make a rough sketch of the graph...Ch. 4.3 - In each part, make a rough sketch of the graph...Ch. 4.3 - Show that y=x+3 is an oblique asymptote of the...Ch. 4.3 - Show that y=3x2 is a curvilinear asymptote of the...Ch. 4.3 - Sketch a graph of the rational function and label...Ch. 4.3 - Sketch a graph of the rational function and label...Ch. 4.3 - Sketch a graph of the rational function and label...Ch. 4.3 - Sketch a graph of the rational function and label...Ch. 4.3 - Sketch a graph of the rational function and label...Ch. 4.3 - Sketch a graph of the rational function and label...Ch. 4.3 - In each part, match the function with graphs I-VI....Ch. 4.3 - Sketch the general shape of the graph of y=x1/n,...Ch. 4.3 - Determine whether the statement is true or false....Ch. 4.3 - Determine whether the statement is true or false....Ch. 4.3 - Determine whether the statement is true or false....Ch. 4.3 - Determine whether the statement is true or false....Ch. 4.3 - Give a graph of the function and identify the...Ch. 4.3 - Give a graph of the function and identify the...Ch. 4.3 - Give a graph of the function and identify the...Ch. 4.3 - Give a graph of the function and identify the...Ch. 4.3 - Give a graph of the function and identify the...Ch. 4.3 - Give a graph of the function and identify the...Ch. 4.3 - Give a graph of the function and identify the...Ch. 4.3 - Give a graph of the function and identify the...Ch. 4.3 - Give a graph of the function and identify the...Ch. 4.3 - Give a graph of the function and identify the...Ch. 4.3 - Give a graph of the function and identify the...Ch. 4.3 - Give a graph of the function and identify the...Ch. 4.3 - Give a graph of the function and identify the...Ch. 4.3 - Give a graph of the function and identify the...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Using L'Ho pital's rule (Section 3.6) one can...Ch. 4.3 - Consider the family of curves y=xebxb0 . (a) Use a...Ch. 4.3 - Consider the family of curves y=ebx2b0 . (a) Use a...Ch. 4.3 - (a) Determine whether the following limits exist,...Ch. 4.3 - Consider the family of curves y=xnex2/n, where n...Ch. 4.3 - The accompanying figure shows the graph of the...Ch. 4.3 - Let fx=12xhx, where hx is as given in Exercise 65....Ch. 4.3 - A rectangular plot of land is to be fenced off so...Ch. 4.3 - A box with a square base and open top is to be...Ch. 4.4 - Use the accompanying graph to find the...Ch. 4.4 - Suppose that a function f is continuous on 4,4 and...Ch. 4.4 - Let fx=x33x29x+25 . Use the derivative fx=3x+1x3...Ch. 4.4 - Use the graph to find x-coordinates of the...Ch. 4.4 - Use the graph to find x-coordinates of the...Ch. 4.4 - In each part, sketch the graph of a continuous...Ch. 4.4 - In each part, sketch the graph of a continuous...Ch. 4.4 - Let fx11x,0x10,x=1 Explain why f has a minimum...Ch. 4.4 - Let fxx,0x112,x=0,1 Explain why f has a minimum...Ch. 4.4 - Find the absolute maximum and minimum values of f...Ch. 4.4 - Find the absolute maximum and minimum values of f...Ch. 4.4 - Find the absolute maximum and minimum values of f...Ch. 4.4 - Find the absolute maximum and minimum values of f...Ch. 4.4 - Find the absolute maximum and minimum values of f...Ch. 4.4 - Find the absolute maximum and minimum values of f...Ch. 4.4 - Find the absolute maximum and minimum values of f...Ch. 4.4 - Find the absolute maximum and minimum values of f...Ch. 4.4 - Find the absolute maximum and minimum values of f...Ch. 4.4 - Find the absolute maximum and minimum values of f...Ch. 4.4 - Determine whether the statement is true or false....Ch. 4.4 - Determine whether the statement is true or false....Ch. 4.4 - Determine whether the statement is true or false....Ch. 4.4 - Determine whether the statement is true or false....Ch. 4.4 - Find the absolute maximum and minimum values of f,...Ch. 4.4 - Find the absolute maximum and minimum values of f,...Ch. 4.4 - Find the absolute maximum and minimum values of f,...Ch. 4.4 - Find the absolute maximum and minimum values of f,...Ch. 4.4 - Find the absolute maximum and minimum values of f,...Ch. 4.4 - Find the absolute maximum and minimum values of f,...Ch. 4.4 - Find the absolute maximum and minimum values of f,...Ch. 4.4 - Find the absolute maximum and minimum values of f,...Ch. 4.4 - Use a graphing utility to estimate the absolute...Ch. 4.4 - Use a graphing utility to estimate the absolute...Ch. 4.4 - Use a graphing utility to estimate the absolute...Ch. 4.4 - Use a graphing utility to estimate the absolute...Ch. 4.4 - Use a graphing utility to estimate the absolute...Ch. 4.4 - Use a graphing utility to estimate the absolute...Ch. 4.4 - Use a graphing utility to estimate the absolute...Ch. 4.4 - Use a graphing utility to estimate the absolute...Ch. 4.4 - Use a graphing utility to estimate the absolute...Ch. 4.4 - Use a graphing utility to estimate the absolute...Ch. 4.4 - Use a graphing utility to estimate the absolute...Ch. 4.4 - Use a graphing utility to estimate the absolute...Ch. 4.4 - Use a graphing utility to estimate the absolute...Ch. 4.4 - Use a graphing utility to estimate the absolute...Ch. 4.4 - Find the absolute maximum and minimum values of...Ch. 4.4 - Let fx=x2+px+q . Find the values of p and q such...Ch. 4.4 - If f is a periodic function, then the locations of...Ch. 4.4 - If f is a periodic function, then the locations of...Ch. 4.4 - One way of proving that fxgx for all x in a given...Ch. 4.4 - One way of proving that fxgx for all x in a given...Ch. 4.4 - What is the smallest possible slope for a tangent...Ch. 4.4 - (a) Show that fx=secx+cscx has a minimum value but...Ch. 4.4 - Show that the absolute minimum value of...Ch. 4.4 - The concentration Ct of a drug in the bloodstream...Ch. 4.4 - A rectangular poster has one side of length x...Ch. 4.4 - A small soft drink can is designed to have volume...Ch. 4.4 - At a construction site, a worker raises an 8-foot...Ch. 4.4 - In the context of Exercise 55, suppose that 0AB...Ch. 4.4 - Suppose that the equations of motion of a paper...Ch. 4.4 - The accompanying figure on the next page shows the...Ch. 4.4 - Let fx=ax2+bx+c, where a0 . Prove that fx0 for all...Ch. 4.4 - Prove Theorem 4.4.3 in the case where the extreme...Ch. 4.4 - Suppose that f is continuous and positive-valued...Ch. 4.5 - A positive number x and its reciprocal are added...Ch. 4.5 - Two nonnegative numbers, x and y, have a sum equal...Ch. 4.5 - A rectangle in the xy-plane has one comer at the...Ch. 4.5 - An open box is to be made from a 20-inch by...Ch. 4.5 - Find a number in the closed interval 12,32 such...Ch. 4.5 - How should two nonnegative numbers be chosen so...Ch. 4.5 - A rectangular field is to be bounded by a fence on...Ch. 4.5 - The boundary of a field is a right triangle with a...Ch. 4.5 - A rectangular plot of land is to be fenced in...Ch. 4.5 - A rectangle is to be inscribed in a right triangle...Ch. 4.5 - Solve the problem in Exercise 6 assuming the...Ch. 4.5 - A rectangle has its two lower comers on the x-axis...Ch. 4.5 - Find the dimensions of the rectangle with maximum...Ch. 4.5 - Find the point P in the first quadrant on the...Ch. 4.5 - A rectangular area of 3200ft2 is to be fenced off....Ch. 4.5 - Show that among all rectangles with perimeter p,...Ch. 4.5 - Show that among all rectangles with area A, the...Ch. 4.5 - A wire of length 12in can be bent into a circle,...Ch. 4.5 - A rectangle R in the plane has comers at 8,12, and...Ch. 4.5 - Solve the problem in Exercise 15 if S is a 16 by...Ch. 4.5 - Solve the problem in Exercise 15 if S is...Ch. 4.5 - A rectangular page is to contain 42 square inches...Ch. 4.5 - A box with a square base is taller than it is...Ch. 4.5 - A box with a square base is wider than it is tall....Ch. 4.5 - An open box is to be made from a 3ft by 8ft...Ch. 4.5 - A closed rectangular container with a square base...Ch. 4.5 - A closed rectangular container with a square base...Ch. 4.5 - A container with square base, vertical sides, and...Ch. 4.5 - A rectangular container with two square sides and...Ch. 4.5 - A church window consisting of a rectangle topped...Ch. 4.5 - Find the dimensions of the right circular cylinder...Ch. 4.5 - Find the dimensions of the right circular cylinder...Ch. 4.5 - A closed, cylindrical can is to have a volume of V...Ch. 4.5 - A closed cylindrical can is to have a surface area...Ch. 4.5 - A cylindrical can, open at the top, is to hold...Ch. 4.5 - A soup can in the shape of a right circular...Ch. 4.5 - A box-shaped wire frame consists of two identical...Ch. 4.5 - Suppose that the sum of the surface areas of a...Ch. 4.5 - Find the height and radius of the cone of slant...Ch. 4.5 - A cone is made from a circular sheet of radius R...Ch. 4.5 - A cone-shaped paper drinking cup is to hold 100cm3...Ch. 4.5 - Find the dimensions of the isosceles triangle of...Ch. 4.5 - Find the height and radius of the right circular...Ch. 4.5 - A commercial cattle ranch currently allows 20...Ch. 4.5 - Prob. 41ESCh. 4.5 - A fertilizer producer finds that it can sell its...Ch. 4.5 - (a) A chemical manufacturer sells sulfuric acid in...Ch. 4.5 - A firm determines that x units of its product can...Ch. 4.5 - In a certain chemical manufacturing process, the...Ch. 4.5 - An independent truck driver charges a client $15...Ch. 4.5 - A trapezoid is inscribed in a semicircle of radius...Ch. 4.5 - A drainage channel is to be made so that its cross...Ch. 4.5 - A lamp is suspended above the center of a round...Ch. 4.5 - A plank is used to reach over a fence 8ft high to...Ch. 4.5 - Two particles, A and B, are in motion in the...Ch. 4.5 - Follow the directions of Exercise 51, with...Ch. 4.5 - Find the coordinates of the point P on the curve...Ch. 4.5 - Find the x-coordinate of the point P on the...Ch. 4.5 - Where on the curve y=1+x21 does the tangent line...Ch. 4.5 - Suppose that the number of bacteria in a culture...Ch. 4.5 - The shoreline of Circle Lake is a circle with...Ch. 4.5 - A man is floating in a rowboat 1 mile from the...Ch. 4.5 - A pipe of negligible diameter is to be carried...Ch. 4.5 - A concrete barrier whose cross section is an...Ch. 4.5 - Suppose that the intensity of a point light source...Ch. 4.5 - Given points A2,1 and B5,4, find the point P in...Ch. 4.5 - The lower edge of a painting, 10ft in height, is...Ch. 4.5 - Fermat’s principle (biography on p.213 ) in...Ch. 4.5 - Fermat’s principle (Exercise 64) also explains...Ch. 4.5 - A farmer wants to walk at a constant rate from her...Ch. 4.5 - Prob. 67ESCh. 4.5 - Prove: If fx0 on an interval and if fx has a...Ch. 4.6 - For a particle in rectilinear motion, the velocity...Ch. 4.6 - Suppose that a particle moving along the s-axis...Ch. 4.6 - A particle in rectilinear motion is speeding up if...Ch. 4.6 - Suppose that a particle moving along the s-axis...Ch. 4.6 - The graphs of three position functions are shown...Ch. 4.6 - The graphs of three velocity functions are shown...Ch. 4.6 - The graph of the position function of a particle...Ch. 4.6 - For the graphs in the accompanying figure, match...Ch. 4.6 - Sketch a reasonable graph of s versus t for a...Ch. 4.6 - The accompanying figure shows the position versus...Ch. 4.6 - The accompanying figure shows the graph of...Ch. 4.6 - The accompanying figure (on the next page) shows...Ch. 4.6 - Determine whether the statement is true or false....Ch. 4.6 - Prob. 10ESCh. 4.6 - Determine whether the statement is true or false....Ch. 4.6 - Determine whether the statement is true or false....Ch. 4.6 - The accompanying figure shows the velocity versus...Ch. 4.6 - The accompanying figure shows the velocity versus...Ch. 4.6 - The function st describes the position of a...Ch. 4.6 - The function st describes the position of a...Ch. 4.6 - The function st describes the position of a...Ch. 4.6 - The function st describes the position of a...Ch. 4.6 - The function st describes the position of a...Ch. 4.6 - The function st describes the position of a...Ch. 4.6 - The function st describes the position of a...Ch. 4.6 - The function st describes the position of a...Ch. 4.6 - Let st=t/t2+5 be the position function of a...Ch. 4.6 - Prob. 24ESCh. 4.6 - A position function of a particle moving along a...Ch. 4.6 - A position function of a particle moving along a...Ch. 4.6 - A position function of a particle moving along a...Ch. 4.6 - A position function of a particle moving along a...Ch. 4.6 - A position function of a particle moving along a...Ch. 4.6 - A position function of a particle moving along a...Ch. 4.6 - A position function of a particle moving along a...Ch. 4.6 - A position function of a particle moving along a...Ch. 4.6 - Let st=5t222t be the position function of a...Ch. 4.6 - Let s=100/t2+12 be the position function of a...Ch. 4.6 - A position function of a particle moving along a...Ch. 4.6 - A position function of a particle moving along a...Ch. 4.6 - Let s=2t2+1 be the position function of a particle...Ch. 4.6 - (a) Use the chain rule to show that for a particle...Ch. 4.6 - Suppose that the position functions of two...Ch. 4.6 - Let sA=15t2+10t+20 and sB=5t2+40t,t0, be the...Ch. 4.6 - Prove that a particle is speeding up if the...Ch. 4.7 - Use the accompanying graph to estimate x2 and x3...Ch. 4.7 - Suppose that f1=1 and f1=4 . If Newton’s Method...Ch. 4.7 - Suppose we are given that f0=3 and that x2=3 when...Ch. 4.7 - If Newton’s Method is applied to y=ex1 with...Ch. 4.7 - In this exercise set, express your answers with as...Ch. 4.7 - In this exercise set, express your answers with as...Ch. 4.7 - In this exercise set, express your answers with as...Ch. 4.7 - In this exercise set, express your answers with as...Ch. 4.7 - The given equation has one real solution....Ch. 4.7 - The given equation has one real solution....Ch. 4.7 - The given equation has one real solution....Ch. 4.7 - The given equation has one real solution....Ch. 4.7 - Use a graphing utility to determine how many...Ch. 4.7 - Use a graphing utility to determine how many...Ch. 4.7 - Use a graphing utility to determine how many...Ch. 4.7 - Use a graphing utility to determine how many...Ch. 4.7 - Use a graphing utility to determine how many...Ch. 4.7 - Use a graphing utility to determine how many...Ch. 4.7 - Use a graphing utility to determine the number of...Ch. 4.7 - Use a graphing utility to determine the number of...Ch. 4.7 - Use a graphing utility to determine the number of...Ch. 4.7 - Use a graphing utility to determine the number of...Ch. 4.7 - Use a graphing utility to determine the number of...Ch. 4.7 - Use a graphing utility to determine the number of...Ch. 4.7 - Determine whether the statement is true or false....Ch. 4.7 - Determine whether the statement is true or false....Ch. 4.7 - Determine whether the statement is true or false....Ch. 4.7 - Determine whether the statement is true or false....Ch. 4.7 - The mechanic’s rule for approximating square...Ch. 4.7 - Many calculators compute reciprocals using the...Ch. 4.7 - Use Newton’s Method to approximate the absolute...Ch. 4.7 - Use Newton’s Method to approximate the absolute...Ch. 4.7 - For the function fx=ex1+x2 use Newton’s Method...Ch. 4.7 - Use Newton’s Method to approximate the absolute...Ch. 4.7 - Use Newton’s Method to approximate the...Ch. 4.7 - Use Newton’s Method to approximate the...Ch. 4.7 - (a) Show that on a circle of radius r, the central...Ch. 4.7 - A segment of a circle is the region enclosed by an...Ch. 4.7 - A walker exercises on an elliptical track given by...Ch. 4.7 - A 6-inch tall plastic “bubble� sits on a flat...Ch. 4.7 - Use Newton’s Method to approximate all real...Ch. 4.7 - Use Newton’s Method to approximate all real...Ch. 4.7 - An annuity is a sequence of equal payments that...Ch. 4.7 - (a) Use a graphing utility to generate the graph...Ch. 4.7 - (a) Apply Newton’s Method to fx=x2+1 with a...Ch. 4.7 - In each part, explain what happens if you apply...Ch. 4.7 - Compare Newton’s Method and the...Ch. 4.8 - Let fx=x2x . (a) An interval on which f satisfies...Ch. 4.8 - Use the accompanying graph of f to find an...Ch. 4.8 - Let fx=x2x . (a) Find a point b such that the...Ch. 4.8 - Use the graph of f in the accompanying figure to...Ch. 4.8 - Find a function f such that the graph of f...Ch. 4.8 - Verify that the hypotheses of Rolle’s Theorem...Ch. 4.8 - Verify that the hypotheses of Rolle’s Theorem...Ch. 4.8 - Verify that the hypotheses of Rolle’s Theorem...Ch. 4.8 - Prob. 4ESCh. 4.8 - Verify that the hypotheses of the Mean-Value...Ch. 4.8 - Verify that the hypotheses of the Mean-Value...Ch. 4.8 - Verify that the hypotheses of the Mean-Value...Ch. 4.8 - Verify that the hypotheses of the Mean-Value...Ch. 4.8 - Prob. 9ESCh. 4.8 - Let fx=x34x . (a) Find the equation of the secant...Ch. 4.8 - Determine whether the statement is true or false....Ch. 4.8 - Determine whether the statement is true or false....Ch. 4.8 - Determine whether the statement is true or false....Ch. 4.8 - Determine whether the statement is true or false....Ch. 4.8 - Let fx=tanx . (a) Show that there is no point c in...Ch. 4.8 - Let fx=x2/3,a=1, and b=8 . (a) Show that there is...Ch. 4.8 - (a) Show that if f is differentiable on ,+, and if...Ch. 4.8 - Review Formulas (6) and (7) in Section 2.1 and use...Ch. 4.8 - Use the result of Exercise 18 in these exercises....Ch. 4.8 - Use the result of Exercise 18 in these exercises....Ch. 4.8 - Suppose that two runners in a 100m dash finish in...Ch. 4.8 - Use the fact that ddxxln2x=ln2xx2x to show that...Ch. 4.8 - (a) Use the Constant Difference Theorem (4.8.3) to...Ch. 4.8 - (a) Use the Constant Difference Theorem (4.8.3) to...Ch. 4.8 - Let gx=xexex . Find fx so that fx=gx and f1=2 .Ch. 4.8 - Let gx=tan1x . Find fx so that fx=gx and f1=2 .Ch. 4.8 - (a) Use the Mean-Value Theorem to show that if f...Ch. 4.8 - (a) Use the Mean-Value Theorem to show that if f...Ch. 4.8 - (a) Use the Mean-Value Theorem to show that yxyx2x...Ch. 4.8 - Show that if f is differentiable on an open...Ch. 4.8 - Use the result in Exercise 30 to show the...Ch. 4.8 - Use the inequality 31.8 to prove that 1.731.75Ch. 4.8 - Use the Mean-Value Theorem to prove that...Ch. 4.8 - (a) Show that if f and g are functions for which...Ch. 4.8 - (a) Show that if f and g are functions for which...Ch. 4.8 - Let f and g be continuous on a,b and...Ch. 4.8 - Illustrate the result in Exercise 36 by drawing an...Ch. 4.8 - (a) Prove that if fx0 for all x in a,b, then fx=0...Ch. 4.8 - (a) Prove part b of Theorem 4.1.2. (b) Prove part...Ch. 4.8 - Use the Mean-Value Theorem to prove the following...Ch. 4.8 - Let fx=3x2,x1ax+b,x1 Find the values of a and b so...Ch. 4.8 - (a) Let fx=x2,x0x2+1,00 Show that limx0fx=limx0+fx...Ch. 4.8 - Use the Mean-Value Theorem to prove the following...Ch. 4 - (a) If x1x2, what relationship must hold between...Ch. 4 - (a) What condition on f ensures that f is concave...Ch. 4 - Find: (a) the intervals on which f is increasing,...Ch. 4 - Find: (a) the intervals on which f is increasing,...Ch. 4 - Find: (a) the intervals on which f is increasing,...Ch. 4 - Find: (a) the intervals on which f is increasing,...Ch. 4 - Find: (a) the intervals on which f is increasing,...Ch. 4 - Find: (a) the intervals on which f is increasing,...Ch. 4 - Find: (a) the intervals on which f is increasing,...Ch. 4 - Find: (a) the intervals on which f is increasing,...Ch. 4 - Analyze the trigonometric function f over the...Ch. 4 - Analyze the trigonometric function f over the...Ch. 4 - Analyze the trigonometric function f over the...Ch. 4 - Analyze the trigonometric function f over the...Ch. 4 - In each part, sketch a continuous curve y=fx with...Ch. 4 - In parts (a)-(d), the graph of a polynomial with...Ch. 4 - For a general quadratic polynomial fx=ax2+bx+ca0...Ch. 4 - For the general cubic polynomial fxax3+bx2+cx+da0...Ch. 4 - Use a graphing utility to estimate the value of x...Ch. 4 - Prove that for any positive constants a and k, the...Ch. 4 - (a) Where on the graph of y=fx would you expect y...Ch. 4 - Determine whether the statement is true or false....Ch. 4 - (a) According to the first derivative test, what...Ch. 4 - Locate the critical points and identify which...Ch. 4 - Locate the critical points and identify which...Ch. 4 - Locate the critical points and identify which...Ch. 4 - In each part, find all critical points, and use...Ch. 4 - In each part, find all critical points, and use...Ch. 4 - Give a graph of the function f, and identify the...Ch. 4 - Give a graph of the function f, and identify the...Ch. 4 - Give a graph of the function f, and identify the...Ch. 4 - Give a graph of the function f, and identify the...Ch. 4 - Give a graph of the function f, and identify the...Ch. 4 - Give a graph of the function f, and identify the...Ch. 4 - Give a graph of the function f, and identify the...Ch. 4 - Give a graph of the function f, and identify the...Ch. 4 - Use any method to find the relative extrema of the...Ch. 4 - Use any method to find the relative extrema of the...Ch. 4 - Use any method to find the relative extrema of the...Ch. 4 - Use any method to find the relative extrema of the...Ch. 4 - Use any method to find the relative extrema of the...Ch. 4 - Use any method to find the relative extrema of the...Ch. 4 - Use any method to find the relative extrema of the...Ch. 4 - Use any method to find the relative extrema of the...Ch. 4 - (a) Use a graphing utility to generate the graphs...Ch. 4 - Use implicit differentiation to show that a...Ch. 4 - Let fx=2x3+x215x+72x13x2+x1 Graph y=fx, and find...Ch. 4 - Let fx=x5x43x3+2x+4x72x63x5+6x4+4x8 (a) Use a CAS...Ch. 4 - (a) What inequality must fx satisfy for the...Ch. 4 - According to the Extreme-Value Theorem, what...Ch. 4 - In each part, determine whether the statement is...Ch. 4 - In each part, find the absolute minimum m and the...Ch. 4 - In each part, find the absolute minimum m and the...Ch. 4 - In each part, find the absolute minimum m and the...Ch. 4 - In each part, use a graphing utility to estimate...Ch. 4 - Prob. 58RECh. 4 - Let fx=x3+2x4+1 (a) Generate the graph of y=fx,...Ch. 4 - A church window consists of a blue semicircular...Ch. 4 - Find the dimensions of the rectangle of maximum...Ch. 4 - As shown in the accompanying figure on the next...Ch. 4 - A sheet of cardboard 12in square is used to make...Ch. 4 - Is it true or false that a particle in rectilinear...Ch. 4 - (a) Can an object in rectilinear motion reverse...Ch. 4 - Suppose that the position function of a particle...Ch. 4 - For parts (a)-(f), suppose that the position...Ch. 4 - Use Newton’s Method to approximate all three...Ch. 4 - Use Newton’s Method to approximate the smallest...Ch. 4 - Use a graphing utility to determine the number of...Ch. 4 - According to Kepler’s law, the planets in our...Ch. 4 - Using the formulas in Exercise 72, find the...Ch. 4 - Suppose that f is continuous on the closed...Ch. 4 - Prob. 75RECh. 4 - In each part, determine whether all of the...Ch. 4 - Use the fact that ddxx62x2+x=6x54x+1 to show that...Ch. 4 - Let fx=x34x+6 . Find fx so that fx=gx and f1=2 .

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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY