::/:;;(((;;::/((;;;;:/—(()(() The derivative of a function is given byf'(z) = (1²-21 - 8)g(x)for some unspecified function g such thatg(z) > 0 for all z: At which point(s) doesf have a local minimum?1. local minimum at x = 42. local minimum at x = -43. local minimum at x = -24. local minimum at r = -2,5. local minimum at r = 24

The first derivative of a function is given by fx = x2-2x-8gx, gx>0 To determine: The point…

Answered: The derivative of a function is given…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 15T

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bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
Q1) Check the continuity of the given function at the given c (or c's). 2 if z+3 (a) f(=) = { -3 c= 3 5 if 1= 3 1+z if zS -2 (b) f(x) = { 2-z if -2 2 Q2) Find the derivative of each function. f). f(e} = In(sec8 + tan 8) 8) f(z) = In () „a) f(z) = %3D b) f(z) = sin %3D %3D 1+cosz c) f(z) = tsinz d) f(z) = (1+z)*(1 – 2)² h) y = (In(ax))² 1+conz g(z) = In(r³ – 3z + 2) i) ) iy = %3D e) f(z) = 19 – 16 +-4 Q3) 27-30 Differentiate f and find the domain of f. 7. f(x) = 28. F(x) = /2 + In x (I – x)u – 1 22. f(x) = In(x² – 2x) 30. (x) = In In In x
Find the point on the curve g(x) = x² – 2 that is closest to the point (3,-2)
Let f(x) and its linear derivative f'(x) be defined for all real numbers. Use the table of selected values to determine f(5). x 2 3 4 5 f(x)-1? -13 ? f'(x)-4-6 ? -10 -19 0-22 O-23 O-31
Consider the function: y = 4—¹ln(x). Find the derivative of the function: y (x) = The domain for this function satisfies < x < If either endpoint is infinite, then write either "-infinity" or "infinity" for that endpoint. Find the vertical asymptote, x = The x-intercept is x = The y-intercept is y = (if no y-intercept exists, then type None''). Find the horizontal asymptote, y = Critical point x (If there is no critical point, then type "None" for both answers): Xc y(x) = This is a relative maximum or minimum? (Max or Min or None) You should make a sketch of this graph with the information that you have found above on a piece of paper. =
2. a. f(x) = (x+2)/(x +4). Use the Mean Value Theorem on the interval [0, 4] to find all values of x in the interval (0, 4) such that the value of the first derivative of f at those points is (f(b) – f(a))/(b – a). b. For the interval [-5, 0], fb) - fa))(b — а)-GG0) — f-5)(0 — (-5)) = (½ – 3)/(0 + 5) = -½ but, since the first derivative of f(x) is always positive, nowhere on that interval does the first derivative of f(x) = -½. Thus the Mean Value Theorem does not hold for f(x) on this interval. Why?
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Let f be a function defined on the closed interval -5 < x 5 5 with f(1) = 3. The graph of f', the derivative of f, consists of two semicircles and two line segments, as shown above. (2, 2) 2 (a) For -5 < x < 5, find all values x at which f has a relative maximum. Justify your answer. -5 -4 -3 -2 -1 0 A 2 3 45 (b) For -5 < x < 5, find all values x at which the graph of f has a point of inflection. Justify your answer. (5, –1) (c) Find all intervals on which the graph of f is concave up and also has positive slope. Explain your reasoning. Graph of f"
Suppose the derivative of the function y = f(x) is y = x/5 (x +5). Determine the intervals on which f(x) is increasing and decreasing. Decreasing on (-5,0); increasing on (-o, -5) U (0, 0) Decreasing on (-5,0); increasing on (0, o) Decreasing on (-o0, -5) U (0, 0): increasing on (-5, 0) Increasing on (-5, 0) O O
8) Find the derivative of the function f(x) = (2x-1 x² + 1 if x ≤0 if x>0
Let f (x) = a +x² 3x - Ca) Determine the y intercept of f(x) and any symmetry. (Don't ind the x-intercepts.) (b) Use the first derivative to determine the relative maximums minimums and intervals of increase/decrease of f(x). You do not need to submit a sign chart or other work. (c) Use the second derivative to determine the points of inflection and intervals of concavity of f(x). You do not need to submit a sign chart or other work.
23 The derivative of the function f(x) = x* + is 23 4x3 (x2) 23 + (æ³) 4x3 23 4x3 + (x) 1 4x 23 4x + 23

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