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(a) Suppose that the first derivative of the function y = f (x) is given by f'(x) = 6(x +1)(x – 2)² 3 At what points, if any, does the graph of f have: • a critical point; • an extreme value; • a point of inflection. (b) Repeat this exercise for the function y = g(x) with derivative g'(x) = 6x(x + 1)(x – 2). Recover the function g, assuming that g(0) = 2.

(a) Suppose that the first derivative of the function y = f (x) is given by f'(x) = 6(x +1)(x – 2)² 3 At what points, if any, does the graph of f have: • a critical point; • an extreme value; • a point of inflection. (b) Repeat this exercise for the function y = g(x) with derivative g'(x) = 6x(x + 1)(x – 2). Recover the function g, assuming that g(0) = 2.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Iunction convex, and wnere is it COI Problem 5 (10 + 1v (a) Suppose that the first derivative of the function y = f (x) is given by 00 noints) f'(x) = 6(x + 1)(x – 2)2 At what points, if any, does the graph of f have: • a critical point; • an extreme value; • a point of inflection. (b) Repeat this exercise for the function y = g(x) with derivative g'(x) = 6x(x + 1)(x – 2). - Recover the function g, assuming that g(0) = 2.
Transcribed Image Text:Iunction convex, and wnere is it COI Problem 5 (10 + 1v (a) Suppose that the first derivative of the function y = f (x) is given by 00 noints) f'(x) = 6(x + 1)(x – 2)2 At what points, if any, does the graph of f have: • a critical point; • an extreme value; • a point of inflection. (b) Repeat this exercise for the function y = g(x) with derivative g'(x) = 6x(x + 1)(x – 2). - Recover the function g, assuming that g(0) = 2.
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