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1. 9. -2 a. Given p(x) = f³(x). Find p '(3) b. Given h(x) =f(g(x)), find h'(3)

1. 9. -2 a. Given p(x) = f³(x). Find p '(3) b. Given h(x) =f(g(x)), find h'(3)

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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The image contains a table and two mathematical problems. ### Table: The table consists of 6 rows and 5 columns. The columns are labeled as \( x \), \( f(x) \), \( f'(x) \), \( g(x) \), and \( g'(x) \). | \( x \) | \( f(x) \) | \( f'(x) \) | \( g(x) \) | \( g'(x) \) | |---------|------------|-------------|------------|-------------| | 1 | 5 | -1 | 1 | 2 | | 2 | 4 | 1 | 3 | \(\frac{3}{2}\) | | 3 | 1 | 1 | 5 | 1 | | 4 | 2 | -1 | 6 | -1 | | 5 | 3 | 0 | 4 | -\(\frac{1}{2}\) | | 6 | 2 | 1 | 1 | -2 | ### Problems: **10.** a. Given \( p(x) = f^3(x) \), find \( p'(3) \). b. Given \( h(x) = f(g(x)) \), find \( h'(3) \). ### Explanation: - **Graph/Diagram Details**: The table contains data for various values of \( x \), including the function values \( f(x) \), its derivative \( f'(x) \), another function \( g(x) \), and its derivative \( g'(x) \). - **Problems Explanation**: - **Part a** involves applying the chain rule or other differentiation techniques to find \( p'(x) \) when \( p(x) = f^3(x) \). - **Part b** also involves differentiation, focusing on finding \( h'(3) \) for the composite function \( h(x) = f(g(x)) \). This can be approached by using the chain rule.
Transcribed Image Text:The image contains a table and two mathematical problems. ### Table: The table consists of 6 rows and 5 columns. The columns are labeled as \( x \), \( f(x) \), \( f'(x) \), \( g(x) \), and \( g'(x) \). | \( x \) | \( f(x) \) | \( f'(x) \) | \( g(x) \) | \( g'(x) \) | |---------|------------|-------------|------------|-------------| | 1 | 5 | -1 | 1 | 2 | | 2 | 4 | 1 | 3 | \(\frac{3}{2}\) | | 3 | 1 | 1 | 5 | 1 | | 4 | 2 | -1 | 6 | -1 | | 5 | 3 | 0 | 4 | -\(\frac{1}{2}\) | | 6 | 2 | 1 | 1 | -2 | ### Problems: **10.** a. Given \( p(x) = f^3(x) \), find \( p'(3) \). b. Given \( h(x) = f(g(x)) \), find \( h'(3) \). ### Explanation: - **Graph/Diagram Details**: The table contains data for various values of \( x \), including the function values \( f(x) \), its derivative \( f'(x) \), another function \( g(x) \), and its derivative \( g'(x) \). - **Problems Explanation**: - **Part a** involves applying the chain rule or other differentiation techniques to find \( p'(x) \) when \( p(x) = f^3(x) \). - **Part b** also involves differentiation, focusing on finding \( h'(3) \) for the composite function \( h(x) = f(g(x)) \). This can be approached by using the chain rule.
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