(8) Suppose that f(x) and g(x) are differentiable and one-to-one and f(2) = –1, f'(2) = -3, f(-1) = 3, f'(-1) = -1/2, g(3) = 2, g'(3) = -7 g(2) g(-1) = 4, and g'(-1) = -4. 5, g'(2) = -2, %3D (a) If h(x) = (f o g)(x), find the tangent line to y = h(x) through (3, h(3)). (b) If j(x) = f(x)g(x), find the tangent line to y = j(x) through (2, j(2)). f(x) (c) If k(x) = g(x)' find the tangent line to y = k(x) through (-1, k(-1)). %3D

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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(8) Suppose that f(x) and g(x) are differentiable and one-to-one and f(2) = –1, f'(2) =
-3, f(-1)
g(-1) = 4, and gʻ(-1)
(a) If h(x) = (f o g)(x), find the tangent line to y = h(x) through (3, h(3)).
-7 g(2)
3, f'(-1) = -1/2, g(3)
= -4.
2, g'(3)
5, g'(2)
-2,
(b) If j(x) = f(x)g(x), find the tangent line to y = j(x) through (2, j(2)).
f(x)
find the tangent line to y =
g(x)
(c) If k(x)
k(x) through (-1, k(–1).
Transcribed Image Text:(8) Suppose that f(x) and g(x) are differentiable and one-to-one and f(2) = –1, f'(2) = -3, f(-1) g(-1) = 4, and gʻ(-1) (a) If h(x) = (f o g)(x), find the tangent line to y = h(x) through (3, h(3)). -7 g(2) 3, f'(-1) = -1/2, g(3) = -4. 2, g'(3) 5, g'(2) -2, (b) If j(x) = f(x)g(x), find the tangent line to y = j(x) through (2, j(2)). f(x) find the tangent line to y = g(x) (c) If k(x) k(x) through (-1, k(–1).
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