(x) f"(x) 1 3 1 -1 -9 7 e 5 9 a) Given h(x)= 2x* [f(x)]. find h'(1). =2r% b) Given h(x) = f(e* ), find h' (1). %3D Nww ww

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

The table shows values for \( f(x) \) and its derivative \( f'(x) \) for specific values of \( x \):

| \( x \) | \( f(x) \) | \( f'(x) \) |
|--------|------------|-------------|
| 1      | 3          | 1           |
| -1     | -9         | 7           |
| \( e \) | 5          | 9           |

### Problem Statements

**a)** Given \( h(x) = 2x^{1/3} [f(x)] \), find \( h'(1) \).

**b)** Given \( h(x) = f(e^{x^2}) \), find \( h'(1) \).
Transcribed Image Text:### Table of Values The table shows values for \( f(x) \) and its derivative \( f'(x) \) for specific values of \( x \): | \( x \) | \( f(x) \) | \( f'(x) \) | |--------|------------|-------------| | 1 | 3 | 1 | | -1 | -9 | 7 | | \( e \) | 5 | 9 | ### Problem Statements **a)** Given \( h(x) = 2x^{1/3} [f(x)] \), find \( h'(1) \). **b)** Given \( h(x) = f(e^{x^2}) \), find \( h'(1) \).
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