x f(x) g(x) g'(x) -3 10 -5 -2 10 -3≤x≤-2 positive negative negative positive -2 0 -3 -2 0 The twice-differentiable functions f and g are defined for all real numbers x. Values of f, f, g, and g' for various values of x s defined by h(x) = f(g(x)). Find h'(-3). Show the computations are given in the table above. The function h that lead to your answer.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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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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x
f(x)
f'(x)
g(x)
g'(x)
-3
10
-5
-2
10
-3 ≤x≤-2
positive
negative
negative
positive
2
0
-3
-2
0
The twice-differentiable functions f and g are defined for all real numbers x. Values of f, f, g, and g' for various values of x
are given in the table above. The function h is defined by h(x) = f(g(x)). Find h'(-3). Show the computations
that lead to your answer.
Transcribed Image Text:x f(x) f'(x) g(x) g'(x) -3 10 -5 -2 10 -3 ≤x≤-2 positive negative negative positive 2 0 -3 -2 0 The twice-differentiable functions f and g are defined for all real numbers x. Values of f, f, g, and g' for various values of x are given in the table above. The function h is defined by h(x) = f(g(x)). Find h'(-3). Show the computations that lead to your answer.
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