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A table of values for f, g, f', and g' is given. X -8 -7 -6 f(x) g(x) f'(x) g'(x) -6 -8 -2 -7 -1 -7 (a) If h(x) = f(g(x)), find h'(-8). h'(-8)= (b) If H(x) = g(f(x)), find H'(-8). H'(-8) = -3 -4 -2 -9 -2 0

A table of values for f, g, f', and g' is given. X -8 -7 -6 f(x) g(x) f'(x) g'(x) -6 -8 -2 -7 -1 -7 (a) If h(x) = f(g(x)), find h'(-8). h'(-8)= (b) If H(x) = g(f(x)), find H'(-8). H'(-8) = -3 -4 -2 -9 -2 0

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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**Table of Values for \( f, g, f', \) and \( g' \)** The following table provides values for functions \( f(x) \), \( g(x) \), and their derivatives \( f'(x) \), \( g'(x) \) at specific points \( x \). | \( x \) | \( f(x) \) | \( g(x) \) | \( f'(x) \) | \( g'(x) \) | |--------|--------|--------|---------|---------| | -8 | -6 | -7 | -3 | -9 | | -7 | -8 | -1 | -4 | -2 | | -6 | -2 | -7 | -2 | 0 | **Problems** (a) If \( h(x) = f(g(x)) \), find \( h'(-8) \). \( h'(-8) = \_\_\_\_ \) (b) If \( H(x) = g(f(x)) \), find \( H'(-8) \). \( H'(-8) = \_\_\_\_ \) **Explanation of Problems** - Use the chain rule for differentiation to find the derivatives of the compositions. - For (a), calculate \( h'(-8) \) using \( h(x) = f(g(x)) \). - For (b), calculate \( H'(-8) \) using \( H(x) = g(f(x)) \).
Transcribed Image Text:**Table of Values for \( f, g, f', \) and \( g' \)** The following table provides values for functions \( f(x) \), \( g(x) \), and their derivatives \( f'(x) \), \( g'(x) \) at specific points \( x \). | \( x \) | \( f(x) \) | \( g(x) \) | \( f'(x) \) | \( g'(x) \) | |--------|--------|--------|---------|---------| | -8 | -6 | -7 | -3 | -9 | | -7 | -8 | -1 | -4 | -2 | | -6 | -2 | -7 | -2 | 0 | **Problems** (a) If \( h(x) = f(g(x)) \), find \( h'(-8) \). \( h'(-8) = \_\_\_\_ \) (b) If \( H(x) = g(f(x)) \), find \( H'(-8) \). \( H'(-8) = \_\_\_\_ \) **Explanation of Problems** - Use the chain rule for differentiation to find the derivatives of the compositions. - For (a), calculate \( h'(-8) \) using \( h(x) = f(g(x)) \). - For (b), calculate \( H'(-8) \) using \( H(x) = g(f(x)) \).
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