please find h'(1) based of given h(x)=f(g(x))

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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please find h'(1) based of given h(x)=f(g(x))

The table provided contains the following data:

| \( x \) | \( f(x) \) | \( g(x) \) | \( f'(x) \) | \( g'(x) \) |
|---------|----------|----------|------------|------------|
| 1       | 3        | 2        | 4          | 6          |
| 2       | 1        | 8        | 5          | 7          |
| 3       | 7        | 2        | 7          | 9          |

This table presents values for two functions, \( f(x) \) and \( g(x) \), and their respective derivatives \( f'(x) \) and \( g'(x) \) at different points \( x \). 

- When \( x = 1 \):
  - \( f(x) = 3 \)
  - \( g(x) = 2 \)
  - \( f'(x) = 4 \)
  - \( g'(x) = 6 \)

- When \( x = 2 \):
  - \( f(x) = 1 \)
  - \( g(x) = 8 \)
  - \( f'(x) = 5 \)
  - \( g'(x) = 7 \)

- When \( x = 3 \):
  - \( f(x) = 7 \)
  - \( g(x) = 2 \)
  - \( f'(x) = 7 \)
  - \( g'(x) = 9 \)

This data can be used to analyze the behavior of the functions and their rates of change at specific points.
Transcribed Image Text:The table provided contains the following data: | \( x \) | \( f(x) \) | \( g(x) \) | \( f'(x) \) | \( g'(x) \) | |---------|----------|----------|------------|------------| | 1 | 3 | 2 | 4 | 6 | | 2 | 1 | 8 | 5 | 7 | | 3 | 7 | 2 | 7 | 9 | This table presents values for two functions, \( f(x) \) and \( g(x) \), and their respective derivatives \( f'(x) \) and \( g'(x) \) at different points \( x \). - When \( x = 1 \): - \( f(x) = 3 \) - \( g(x) = 2 \) - \( f'(x) = 4 \) - \( g'(x) = 6 \) - When \( x = 2 \): - \( f(x) = 1 \) - \( g(x) = 8 \) - \( f'(x) = 5 \) - \( g'(x) = 7 \) - When \( x = 3 \): - \( f(x) = 7 \) - \( g(x) = 2 \) - \( f'(x) = 7 \) - \( g'(x) = 9 \) This data can be used to analyze the behavior of the functions and their rates of change at specific points.
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