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A table of values for f, g, f', and g is given below. af(x) g(x) | f'(x) g(x) 1 3. 3 1 1 2 1 3 3 1 (A) If h(x) = f(g(x)), then h'(2) = (B) If H(x) = g(f(x)), then H'(2) =

A table of values for f, g, f', and g is given below. af(x) g(x) | f'(x) g(x) 1 3. 3 1 1 2 1 3 3 1 (A) If h(x) = f(g(x)), then h'(2) = (B) If H(x) = g(f(x)), then H'(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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### Table of Values and Calculus Problems A table of values for the functions \( f \), \( g \), and their derivatives \( f' \) and \( g' \) is provided below. | \( x \) | \( f(x) \) | \( g(x) \) | \( f'(x) \) | \( g'(x) \) | |--------|----------|----------|-----------|-----------| | 1 | 3 | 2 | 3 | 2 | | 2 | 1 | 1 | 2 | 1 | | 3 | 3 | 2 | 2 | 1 | #### Problems: (A) If \( h(x) = f(g(x)) \), then find \( h'(2) \). (B) If \( H(x) = g(f(x)) \), then find \( H'(2) \). To solve these problems, apply the chain rule: - For (A): \( h'(x) = f'(g(x)) \cdot g'(x) \) - For (B): \( H'(x) = g'(f(x)) \cdot f'(x) \) Evaluate these derivatives at \( x = 2 \) using the provided table values.
Transcribed Image Text:### Table of Values and Calculus Problems A table of values for the functions \( f \), \( g \), and their derivatives \( f' \) and \( g' \) is provided below. | \( x \) | \( f(x) \) | \( g(x) \) | \( f'(x) \) | \( g'(x) \) | |--------|----------|----------|-----------|-----------| | 1 | 3 | 2 | 3 | 2 | | 2 | 1 | 1 | 2 | 1 | | 3 | 3 | 2 | 2 | 1 | #### Problems: (A) If \( h(x) = f(g(x)) \), then find \( h'(2) \). (B) If \( H(x) = g(f(x)) \), then find \( H'(2) \). To solve these problems, apply the chain rule: - For (A): \( h'(x) = f'(g(x)) \cdot g'(x) \) - For (B): \( H'(x) = g'(f(x)) \cdot f'(x) \) Evaluate these derivatives at \( x = 2 \) using the provided table values.
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