Single Variable Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals
8th Edition
ISBN: 9781305270336
Author: James Stewart
Publisher: Cengage Learning
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Concept explainers

Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
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.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Textbook Question
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Chapter 4.3, Problem 48E

(a) Find the intervals of increase or decrease.

(b) Find the local maximum and minimum values.

(c) Find the intervals of concavity and the inflection points.

(d) Use the information from parts (a)–(c) to sketch the graph. Check your work with a graphing device if you have one.

S(x) = x − sin x, 0 ≤ x ≤ 4π

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Chapter 4.3, Problem 47E
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Chapter 4 Solutions

Single Variable Calculus: Early Transcendentals

Ch. 4.1 - Explain the difference between an absolute minimum...Ch. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - For each of the numbers a, b, c, d, r, and s,...Ch. 4.1 - Prob. 5ECh. 4.1 - Use the graph to state the absolute and local...Ch. 4.1 - Prob. 7ECh. 4.1 - Sketch the graph of a function f that is...Ch. 4.1 - Sketch the graph of a function f that is...Ch. 4.1 - Prob. 10E
Ch. 4.1 - (a) Sketch the graph of a function that has a...Ch. 4.1 - Prob. 12ECh. 4.1 - (a) Sketch the graph of a function on [1, 2] that...Ch. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Sketch the graph of f by hand and use your sketch...Ch. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Sketch the graph of f by hand and use your sketch...Ch. 4.1 - Sketch the graph of f by hand and use your sketch...Ch. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Sketch the graph of f by hand and use your sketch...Ch. 4.1 - Prob. 26ECh. 4.1 - Sketch the graph of f by hand and use your sketch...Ch. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Find the critical numbers of the function. f(x) =...Ch. 4.1 - Find the critical numbers of the function. f(x) =...Ch. 4.1 - Prob. 32ECh. 4.1 - Find the critical numbers of the function. g(t) =...Ch. 4.1 - Prob. 34ECh. 4.1 - Find the critical numbers of the function....Ch. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Find the critical numbers of the function. g() = 4...Ch. 4.1 - Find the critical numbers of the function. f() = 2...Ch. 4.1 - Find the critical numbers of the function. h(t) =...Ch. 4.1 - Find the critical numbers of the function. f(x) =...Ch. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - A formula for the derivative of a function f is...Ch. 4.1 - Prob. 47ECh. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Find the absolute maximum and absolute minimum...Ch. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - Prob. 60ECh. 4.1 - Prob. 61ECh. 4.1 - Prob. 62ECh. 4.1 - Prob. 63ECh. 4.1 - Prob. 64ECh. 4.1 - Prob. 65ECh. 4.1 - Prob. 66ECh. 4.1 - Prob. 67ECh. 4.1 - Prob. 68ECh. 4.1 - Prob. 69ECh. 4.1 - After an antibiotic tablet is taken, the...Ch. 4.1 - Between 0C and 30C, the volume V (in cubic...Ch. 4.1 - Prob. 72ECh. 4.1 - Prob. 73ECh. 4.1 - Prob. 74ECh. 4.1 - Prob. 75ECh. 4.1 - Prob. 76ECh. 4.1 - Prob. 77ECh. 4.1 - Prob. 78ECh. 4.1 - Prob. 79ECh. 4.1 - Prob. 80ECh. 4.2 - The graph of a function f is shown. Verify that f...Ch. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Verify that the function satisfies the three...Ch. 4.2 - Prob. 6ECh. 4.2 - Verify that the function satisfies the three...Ch. 4.2 - Verify that the function satisfies the three...Ch. 4.2 - Let f(x) = 1 x2/3. Show that f(l) = f(1) but...Ch. 4.2 - Prob. 10ECh. 4.2 - Verify that the function satisfies the hypotheses...Ch. 4.2 - Verify that the function satisfies the hypotheses...Ch. 4.2 - Verify that the function satisfies the hypotheses...Ch. 4.2 - Verify that the function satisfies the hypotheses...Ch. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Let f(x) = (x 3)2. Show that there is no value of...Ch. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Show that the equation x3 15x + c = 0 has at most...Ch. 4.2 - Prob. 22ECh. 4.2 - (a) Show that a polynomial of degree 3 has at most...Ch. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 36ECh. 4.2 - Two runners start a race at the same time and...Ch. 4.2 - Prob. 38ECh. 4.3 - Use the given graph of f to find the following....Ch. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - The graph of the derivative f of a function f is...Ch. 4.3 - The graph of the derivative f of a function f is...Ch. 4.3 - In each part state the x-coordinates of the...Ch. 4.3 - The graph of the first derivative f of a function...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - (a) Find the intervals on which f is increasing or...Ch. 4.3 - Find the local maximum and minimum values of f...Ch. 4.3 - Find the local maximum and minimum values of f...Ch. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Sketch the graph of a function that satisfies all...Ch. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - Sketch the graph of a function that satisfies all...Ch. 4.3 - Prob. 31ECh. 4.3 - Suppose f(3) = 2, f(3)=12, and f(x) 0 and f(x) 0...Ch. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - The graph of the derivative f of a continuous...Ch. 4.3 - The graph of the derivative f of a continuous...Ch. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - Prob. 41ECh. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Prob. 47ECh. 4.3 - (a) Find the intervals of increase or decrease....Ch. 4.3 - (a) Find the vertical and horizontal asymptotes....Ch. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - (a) Find the vertical and horizontal asymptotes....Ch. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - (a) Find the vertical and horizontal asymptotes....Ch. 4.3 - Suppose the derivative of a function f is f(x) =...Ch. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 66ECh. 4.3 - The president announces that the national deficit...Ch. 4.3 - Prob. 68ECh. 4.3 - Let K(t) be a measure of the knowledge you gain by...Ch. 4.3 - Prob. 70ECh. 4.3 - Prob. 71ECh. 4.3 - Prob. 72ECh. 4.3 - Find a cubic function f(x) = ax3 + bx2 + cx + d...Ch. 4.3 - Prob. 74ECh. 4.3 - (a) If the function f(x) = x3 + ax2 + bx has the...Ch. 4.3 - Prob. 76ECh. 4.3 - Show that the curve y = (1 + x)/(1 + x2) has three...Ch. 4.3 - Show that the curves y = ex and y = ex touch the...Ch. 4.3 - Prob. 79ECh. 4.3 - Prob. 80ECh. 4.3 - Assume that all of the functions are twice...Ch. 4.3 - Prob. 82ECh. 4.3 - Prob. 83ECh. 4.3 - (a) Show that ex 1 + x for x 0. (b) Deduce that...Ch. 4.3 - Prob. 85ECh. 4.3 - For what values of c does the polynomial P(x) = x4...Ch. 4.3 - Prob. 87ECh. 4.3 - Prob. 88ECh. 4.3 - Prob. 89ECh. 4.3 - Prob. 90ECh. 4.3 - Prob. 92ECh. 4.3 - The three cases in the First Derivative Test cover...Ch. 4.4 - Given that...Ch. 4.4 - Given that...Ch. 4.4 - Prob. 3ECh. 4.4 - Given that...Ch. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - The graph of a function f and its tangent line at...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Prob. 12ECh. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Prob. 20ECh. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Prob. 24ECh. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Prob. 42ECh. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Prob. 46ECh. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Prob. 48ECh. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Prob. 50ECh. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - Prob. 55ECh. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Prob. 57ECh. 4.4 - Prob. 58ECh. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Prob. 61ECh. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Find the limit. Use lHospitals Rule where...Ch. 4.4 - Prob. 66ECh. 4.4 - Prob. 67ECh. 4.4 - Prob. 68ECh. 4.4 - Prob. 69ECh. 4.4 - Prob. 70ECh. 4.4 - Prob. 71ECh. 4.4 - Prob. 72ECh. 4.4 - Prove that limxexxn= for any positive integer n....Ch. 4.4 - Prob. 74ECh. 4.4 - Prob. 75ECh. 4.4 - Prob. 76ECh. 4.4 - Prob. 77ECh. 4.4 - Prob. 78ECh. 4.4 - Prob. 79ECh. 4.4 - Light enters the eye through the pupil and strikes...Ch. 4.4 - Prob. 81ECh. 4.4 - Prob. 82ECh. 4.4 - Prob. 83ECh. 4.4 - Prob. 84ECh. 4.4 - Prob. 85ECh. 4.4 - Prob. 86ECh. 4.4 - Prob. 87ECh. 4.4 - Prob. 88ECh. 4.4 - Prob. 89ECh. 4.4 - Prob. 90ECh. 4.4 - Prob. 91ECh. 4.4 - Let f(x)={xxifx01ifx=0 (a) Show that f is...Ch. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Prob. 21ECh. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - The table gives the population of the world P(t),...Ch. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Prob. 31ECh. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Prob. 37ECh. 4.5 - Prob. 38ECh. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Prob. 40ECh. 4.5 - Prob. 41ECh. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Prob. 49ECh. 4.5 - Prob. 50ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Prob. 53ECh. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - Prob. 57ECh. 4.5 - Prob. 58ECh. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Prob. 61ECh. 4.5 - Prob. 62ECh. 4.5 - Prob. 63ECh. 4.5 - Prob. 64ECh. 4.5 - Prob. 65ECh. 4.5 - Prob. 66ECh. 4.5 - Prob. 67ECh. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Prob. 69ECh. 4.5 - Use the guidelines of this section to sketch the...Ch. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - Prob. 73ECh. 4.5 - Prob. 74ECh. 4.5 - Prob. 75ECh. 4.5 - Prob. 76ECh. 4.6 - Prob. 1ECh. 4.6 - Produce graphs of f that reveal all the important...Ch. 4.6 - Prob. 3ECh. 4.6 - Prob. 4ECh. 4.6 - Prob. 5ECh. 4.6 - Prob. 6ECh. 4.6 - Prob. 9ECh. 4.6 - Prob. 10ECh. 4.6 - Prob. 13ECh. 4.6 - Sketch the graph by hand using asymptotes and...Ch. 4.6 - Prob. 27ECh. 4.6 - Prob. 28ECh. 4.6 - Prob. 29ECh. 4.6 - Prob. 30ECh. 4.6 - Prob. 33ECh. 4.6 - Prob. 34ECh. 4.6 - Prob. 35ECh. 4.6 - Prob. 38ECh. 4.6 - Prob. 39ECh. 4.6 - (a) Investigate the family of polynomials given by...Ch. 4.7 - Consider the following problem: Find two numbers...Ch. 4.7 - Find two numbers whose difference is 100 and whose...Ch. 4.7 - Find two positive numbers whose product is 100 and...Ch. 4.7 - The sum of two positive numbers is 16. What is the...Ch. 4.7 - What is the maximum vertical distance between the...Ch. 4.7 - What is the minimum vertical distance between the...Ch. 4.7 - Find the dimensions of a rectangle with perimeter...Ch. 4.7 - Find the dimensions of a rectangle with area 1000...Ch. 4.7 - Prob. 9ECh. 4.7 - The rate (in mg carbon/m3/h) at which...Ch. 4.7 - Consider the following problem: A farmer with 750...Ch. 4.7 - Prob. 12ECh. 4.7 - Prob. 13ECh. 4.7 - A box with a square base and open top must have a...Ch. 4.7 - If 1200 cm2 of material is available to make a box...Ch. 4.7 - Prob. 16ECh. 4.7 - Prob. 17ECh. 4.7 - A farmer wants to fence in a rectangular plot of...Ch. 4.7 - Prob. 19ECh. 4.7 - Prob. 20ECh. 4.7 - Prob. 21ECh. 4.7 - Find the point on the curve y=x that is closest to...Ch. 4.7 - Find the points on the ellipse 4x2 + y2 = 4 that...Ch. 4.7 - Prob. 24ECh. 4.7 - Find the dimensions of the rectangle of largest...Ch. 4.7 - Find the area of the largest rectangle that can be...Ch. 4.7 - Prob. 27ECh. 4.7 - Prob. 28ECh. 4.7 - Prob. 29ECh. 4.7 - Prob. 30ECh. 4.7 - A right circular cylinder is inscribed in a sphere...Ch. 4.7 - A right circular cylinder is inscribed in a cone...Ch. 4.7 - Prob. 33ECh. 4.7 - A Norman window has the shape of a rectangle...Ch. 4.7 - The top and bottom margins of a poster are each 6...Ch. 4.7 - A poster is to have an area of 180 in2 with 1-inch...Ch. 4.7 - A piece of wire 10 m long is cut into two pieces....Ch. 4.7 - Answer Exercise 37 if one piece is bent into a...Ch. 4.7 - Prob. 39ECh. 4.7 - Prob. 40ECh. 4.7 - A cone-shaped drinking cup is made from a circular...Ch. 4.7 - A cone-shaped paper drinking cup is to be made to...Ch. 4.7 - A cone with height h is inscribed in a larger cone...Ch. 4.7 - An object with weight W is dragged along a...Ch. 4.7 - If a resistor of R ohms is connected across a...Ch. 4.7 - For a fish swimming at a speed v relative to the...Ch. 4.7 - In a beehive, each cell is a regular hexagonal...Ch. 4.7 - Prob. 48ECh. 4.7 - Prob. 49ECh. 4.7 - A woman at a point A on the shore of a circular...Ch. 4.7 - Prob. 51ECh. 4.7 - Prob. 52ECh. 4.7 - The illumination of an object by a light source is...Ch. 4.7 - Prob. 54ECh. 4.7 - Prob. 55ECh. 4.7 - At which points on the curve y = 1 + 40x3 3x5...Ch. 4.7 - Prob. 57ECh. 4.7 - Prob. 58ECh. 4.7 - Prob. 59ECh. 4.7 - (a) Show that if the profit P(x) is a maximum,...Ch. 4.7 - A baseball team plays in a stadium that holds...Ch. 4.7 - During the summer months Terry makes and sells...Ch. 4.7 - A retailer has been selling 1200 tablet computers...Ch. 4.7 - Prob. 64ECh. 4.7 - Show that of all the isosceles triangles with a...Ch. 4.7 - Prob. 66ECh. 4.7 - Prob. 67ECh. 4.7 - Prob. 68ECh. 4.7 - A point P needs to be located somewhere on the...Ch. 4.7 - The graph shows the fuel consumption c of a car...Ch. 4.7 - Prob. 71ECh. 4.7 - Prob. 72ECh. 4.7 - Prob. 73ECh. 4.7 - A steel pipe is being carried down a hallway 9 ft...Ch. 4.7 - Prob. 75ECh. 4.7 - Prob. 76ECh. 4.7 - Prob. 77ECh. 4.7 - A painting in an art gallery has height h and is...Ch. 4.7 - Prob. 79ECh. 4.7 - The blood vascular system consists of blood...Ch. 4.7 - Ornithologists have determined that some species...Ch. 4.7 - Two light sources of identical strength are placed...Ch. 4.8 - The figure shows the graph of a function f....Ch. 4.8 - Follow the instructions for Exercise 1(a) but use...Ch. 4.8 - Suppose the tangent line to the curve y = f(x) at...Ch. 4.8 - For each initial approximation, determine...Ch. 4.8 - For which of the initial approximations x1 = a, b,...Ch. 4.8 - Use Newtons method with the specified initial...Ch. 4.8 - Use Newtons method with the specified initial...Ch. 4.8 - Use Newtons method with the specified initial...Ch. 4.8 - Use Newtons method with initial approximation x1 =...Ch. 4.8 - Use Newtons method with initial approximation x1 =...Ch. 4.8 - Use Newtons method to approximate the given number...Ch. 4.8 - Use Newtons method to approximate the given number...Ch. 4.8 - (a) Explain how we know that the given equation...Ch. 4.8 - (a) Explain how we know that the given equation...Ch. 4.8 - Use Newtons method to approximate the indicated...Ch. 4.8 - Use Newtons method to approximate the indicated...Ch. 4.8 - Use Newtons method to find all solutions of the...Ch. 4.8 - Use Newtons method to find all solutions of the...Ch. 4.8 - Use Newtons method to find all solutions of the...Ch. 4.8 - Use Newtons method to find all solutions of the...Ch. 4.8 - Use Newtons method to find all solutions of the...Ch. 4.8 - Use Newtons method to find all solutions of the...Ch. 4.8 - Use Newtons method to find all the solutions of...Ch. 4.8 - Use Newtons method to find all the solutions of...Ch. 4.8 - Use Newtons method to find all the solutions of...Ch. 4.8 - Use Newtons method to find all the solutions of...Ch. 4.8 - Use Newtons method to find all the solutions of...Ch. 4.8 - (a) Apply Newtons method to the equation x2 a = 0...Ch. 4.8 - (a) Apply Newtons method to the equation 1/x a =...Ch. 4.8 - (a) Use Newtons method with x1 = 1 to find the...Ch. 4.8 - Explain why Newtons method fails when applied to...Ch. 4.8 - If f(x)={xifx0xifx0 then the root of the equation...Ch. 4.8 - (a) Use Newtons method to find the critical...Ch. 4.8 - Use Newtons method to find the absolute maximum...Ch. 4.8 - Use Newtons method to find the coordinates of the...Ch. 4.8 - Use Newtons method to find the coordinates,...Ch. 4.8 - In the figure, the length of the chord AB is 4 cm...Ch. 4.8 - A car dealer sells a new car for 18,000. He also...Ch. 4.8 - The figure shows the sun located at the origin and...Ch. 4.9 - Find the most general antiderivative of the...Ch. 4.9 - Find the most general antiderivative of the...Ch. 4.9 - Prob. 3ECh. 4.9 - Prob. 4ECh. 4.9 - Prob. 5ECh. 4.9 - Find the most general antiderivative of the...Ch. 4.9 - Find the most general antiderivative of the...Ch. 4.9 - Find the most general antiderivative of the...Ch. 4.9 - Find the most general antiderivative of the...Ch. 4.9 - Find the most general antiderivative of the...Ch. 4.9 - Prob. 11ECh. 4.9 - Find the most general antiderivative of the...Ch. 4.9 - Prob. 13ECh. 4.9 - Prob. 14ECh. 4.9 - Find the most general antiderivative of the...Ch. 4.9 - Find the most general antiderivative of the...Ch. 4.9 - Find the most general antiderivative of the...Ch. 4.9 - Prob. 18ECh. 4.9 - Find the most general antiderivative of the...Ch. 4.9 - Prob. 20ECh. 4.9 - Prob. 21ECh. 4.9 - Prob. 22ECh. 4.9 - Find f. f(x) = 20x3 12x2 + 6xCh. 4.9 - Find f. f(x) = x6 4x4 + x + 1Ch. 4.9 - Find f. f(x) = 2x + 3exCh. 4.9 - Find f. f(x) = 1/x2Ch. 4.9 - Find f. f(t) = 12 + sin tCh. 4.9 - Prob. 30ECh. 4.9 - Prob. 31ECh. 4.9 - Find f. f(x) = 5x4 3x2 + 4, f(1) = 2Ch. 4.9 - Prob. 33ECh. 4.9 - Find f. f(t) = t + 1/t3, t 0, f(1) = 6Ch. 4.9 - Find f. f(x) = 5x2/3, f(8) = 21Ch. 4.9 - Prob. 36ECh. 4.9 - Prob. 37ECh. 4.9 - Prob. 38ECh. 4.9 - Prob. 39ECh. 4.9 - Find f. f(x) = 8x3 + 5, f(1) = 0, f(1) = 8Ch. 4.9 - Prob. 41ECh. 4.9 - Prob. 42ECh. 4.9 - Prob. 43ECh. 4.9 - Find f. f(x) = x3 + sinh x, f(0) = 1, f(2) = 2.6Ch. 4.9 - Find f. f(x) = ex 2 sin x, f(0) = 3, f(/2) = 0Ch. 4.9 - Find f. f(t)=t3cost, f(0) = 2, f(1) = 2Ch. 4.9 - Prob. 47ECh. 4.9 - Prob. 48ECh. 4.9 - Prob. 49ECh. 4.9 - Prob. 50ECh. 4.9 - Prob. 51ECh. 4.9 - The graph of a function f is shown. Which graph is...Ch. 4.9 - Prob. 53ECh. 4.9 - Prob. 54ECh. 4.9 - The graph of f is shown in the figure. Sketch the...Ch. 4.9 - Prob. 56ECh. 4.9 - Prob. 57ECh. 4.9 - Prob. 58ECh. 4.9 - A particle is moving with the given data. Find the...Ch. 4.9 - A particle is moving with the given data. Find the...Ch. 4.9 - Prob. 61ECh. 4.9 - A particle is moving with the given data. Find the...Ch. 4.9 - Prob. 63ECh. 4.9 - A particle is moving with the given data. Find the...Ch. 4.9 - Prob. 65ECh. 4.9 - Prob. 66ECh. 4.9 - Prob. 67ECh. 4.9 - Prob. 68ECh. 4.9 - Prob. 69ECh. 4.9 - Prob. 70ECh. 4.9 - Prob. 71ECh. 4.9 - Prob. 72ECh. 4.9 - Since raindrops grow as they fall, their surface...Ch. 4.9 - Prob. 74ECh. 4.9 - Prob. 75ECh. 4.9 - Prob. 76ECh. 4.9 - Prob. 77ECh. 4.9 - Prob. 79ECh. 4 - Prob. 1RCCCh. 4 - Prob. 2RCCCh. 4 - Prob. 3RCCCh. 4 - Prob. 4RCCCh. 4 - Prob. 5RCCCh. 4 - Prob. 6RCCCh. 4 - Prob. 7RCCCh. 4 - State whether each of the following limit forms is...Ch. 4 - Prob. 9RCCCh. 4 - Prob. 10RCCCh. 4 - Prob. 11RCCCh. 4 - Prob. 1RQCh. 4 - Prob. 2RQCh. 4 - Prob. 3RQCh. 4 - Prob. 4RQCh. 4 - Prob. 5RQCh. 4 - Prob. 6RQCh. 4 - Prob. 7RQCh. 4 - Prob. 8RQCh. 4 - Prob. 9RQCh. 4 - Prob. 10RQCh. 4 - Prob. 11RQCh. 4 - Prob. 12RQCh. 4 - Prob. 13RQCh. 4 - If f and g are positive increasing functions on an...Ch. 4 - Prob. 15RQCh. 4 - Prob. 16RQCh. 4 - Prob. 17RQCh. 4 - Prob. 18RQCh. 4 - If f(x) exists and is nonzero for all x, then f(1)...Ch. 4 - Prob. 20RQCh. 4 - limx0xex=1Ch. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - The figure shows the graph of the derivative f of...Ch. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Find the point on the hyperbola xy = 8 that is...Ch. 4 - Find the smallest possible area of an isosceles...Ch. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - Prob. 58RECh. 4 - Prob. 59RECh. 4 - A manufacturer determines that the cost of making...Ch. 4 - Prob. 61RECh. 4 - Prob. 62RECh. 4 - Prob. 63RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RECh. 4 - Prob. 70RECh. 4 - Prob. 71RECh. 4 - Prob. 72RECh. 4 - Prob. 73RECh. 4 - Prob. 74RECh. 4 - (a) If f(x) = 0.1ex + sin x, 4 x 4, use a graph...Ch. 4 - Prob. 76RECh. 4 - Prob. 77RECh. 4 - Prob. 78RECh. 4 - A rectangular beam will be cut from a cylindrical...Ch. 4 - Prob. 80RECh. 4 - Prob. 81RECh. 4 - Prob. 82RECh. 4 - Prob. 83RECh. 4 - Prob. 84RECh. 4 - Prob. 85RECh. 4 - Prob. 86RECh. 4 - If a rectangle has its base on the x-axis and two...Ch. 4 - Show that sinxcosx2 for all x.Ch. 4 - Prob. 3PCh. 4 - Prob. 4PCh. 4 - Prob. 5PCh. 4 - Find the point on the parabola y = 1 x2 at which...Ch. 4 - Prob. 7PCh. 4 - Prob. 8PCh. 4 - Prob. 9PCh. 4 - Prob. 10PCh. 4 - Prob. 11PCh. 4 - For what values of c does the curve y = cx3 + ex...Ch. 4 - Prob. 13PCh. 4 - Prob. 14PCh. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Prob. 17PCh. 4 - For what value of a is the following equation...Ch. 4 - Prob. 19PCh. 4 - Prob. 20PCh. 4 - The speeds of sound c1 in an upper layer and c2 in...Ch. 4 - Prob. 22PCh. 4 - Prob. 23PCh. 4 - Prob. 25PCh. 4 - Prob. 26P
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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