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let p(x)=g(f(x)). use the given table to find p'4

let p(x)=g(f(x)). use the given table to find p'4

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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let p(x)=g(f(x)). use the given table to find p'4

The table presented is organized with columns and rows, each representing the values of functions and their derivatives at specific points. Here is the detailed transcription: | \( x \) | \( 1 \) | \( 2 \) | \( 3 \) | \( 4 \) | \( 5 \) | |---------|---------|---------|---------|---------|---------| | \( f(x) \) | \( 0 \) | \( 3 \) | \( 5 \) | \( 1 \) | \( 0 \) | | \( f'(x) \) | \( 5 \) | \( 2 \) | \( -5 \) | \( -8 \) | \( -10 \) | | \( g(x) \) | \( 4 \) | \( 5 \) | \( 1 \) | \( 3 \) | \( 2 \) | | \( g'(x) \) | \( 2 \) | \( 10 \) | \( 20 \) | \( 15 \) | \( 20 \) | This table displays the following: 1. \( f(x) \): The values of the function \( f \) at \( x = 1, 2, 3, 4, \) and \( 5 \). 2. \( f'(x) \): The values of the derivative of \( f \), indicating the rate of change of \( f \) at each specified \( x \). 3. \( g(x) \): The values of the function \( g \) at \( x = 1, 2, 3, 4, \) and \( 5 \). 4. \( g'(x) \): The values of the derivative of \( g \), indicating the rate of change of \( g \) at each specified \( x \). Each column represents a specific value of \( x \), and corresponding rows provide the respective function values and their derivatives. This format is useful for analyzing the behavior and trends of the functions and their rates of change.
Transcribed Image Text:The table presented is organized with columns and rows, each representing the values of functions and their derivatives at specific points. Here is the detailed transcription: | \( x \) | \( 1 \) | \( 2 \) | \( 3 \) | \( 4 \) | \( 5 \) | |---------|---------|---------|---------|---------|---------| | \( f(x) \) | \( 0 \) | \( 3 \) | \( 5 \) | \( 1 \) | \( 0 \) | | \( f'(x) \) | \( 5 \) | \( 2 \) | \( -5 \) | \( -8 \) | \( -10 \) | | \( g(x) \) | \( 4 \) | \( 5 \) | \( 1 \) | \( 3 \) | \( 2 \) | | \( g'(x) \) | \( 2 \) | \( 10 \) | \( 20 \) | \( 15 \) | \( 20 \) | This table displays the following: 1. \( f(x) \): The values of the function \( f \) at \( x = 1, 2, 3, 4, \) and \( 5 \). 2. \( f'(x) \): The values of the derivative of \( f \), indicating the rate of change of \( f \) at each specified \( x \). 3. \( g(x) \): The values of the function \( g \) at \( x = 1, 2, 3, 4, \) and \( 5 \). 4. \( g'(x) \): The values of the derivative of \( g \), indicating the rate of change of \( g \) at each specified \( x \). Each column represents a specific value of \( x \), and corresponding rows provide the respective function values and their derivatives. This format is useful for analyzing the behavior and trends of the functions and their rates of change.
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