Find the following using the table below. 1 23 4 f(x) f'(x) 3 1 4 2 3 g(x) g'(x) 2 4 1 1 4 2 3 1 3 4 2 h'(4) if h(x) = f(x) • g(x) f(x) h'(4) if h(x) = g(x) h'(4) if h(x) = f(g(x))
Find the following using the table below. 1 23 4 f(x) f'(x) 3 1 4 2 3 g(x) g'(x) 2 4 1 1 4 2 3 1 3 4 2 h'(4) if h(x) = f(x) • g(x) f(x) h'(4) if h(x) = g(x) h'(4) if h(x) = f(g(x))
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.4: More Quadratic Functions And Applications
Problem 55PS
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Question
![## Problem Statement
Find the following using the table below.
### Table
| \( x \) | 1 | 2 | 3 | 4 |
|---------|---|---|---|---|
| \( f(x) \) | 3 | 1 | 4 | 2 |
| \( f'(x) \) | 3 | 2 | 4 | 1 |
| \( g(x) \) | 1 | 4 | 2 | 3 |
| \( g'(x) \) | 1 | 3 | 4 | 2 |
### Tasks
1. \( h'(4) \) if \( h(x) = f(x) \cdot g(x) \)
- **Solution Box:** [ ]
2. \( h'(4) \) if \( h(x) = \frac{f(x)}{g(x)} \)
- **Solution Box:** [ ]
3. \( h'(4) \) if \( h(x) = f(g(x)) \)
- **Solution Box:** [ ]
---
Use the provided derivatives and function values from the table to solve the above tasks, applying the appropriate differentiation rules for each function composition or operation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F437d091c-bafd-402f-b1ab-0058f5d0273f%2Fc664915d-87f0-4732-ab0e-7df418e2d575%2Fhhx4akx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem Statement
Find the following using the table below.
### Table
| \( x \) | 1 | 2 | 3 | 4 |
|---------|---|---|---|---|
| \( f(x) \) | 3 | 1 | 4 | 2 |
| \( f'(x) \) | 3 | 2 | 4 | 1 |
| \( g(x) \) | 1 | 4 | 2 | 3 |
| \( g'(x) \) | 1 | 3 | 4 | 2 |
### Tasks
1. \( h'(4) \) if \( h(x) = f(x) \cdot g(x) \)
- **Solution Box:** [ ]
2. \( h'(4) \) if \( h(x) = \frac{f(x)}{g(x)} \)
- **Solution Box:** [ ]
3. \( h'(4) \) if \( h(x) = f(g(x)) \)
- **Solution Box:** [ ]
---
Use the provided derivatives and function values from the table to solve the above tasks, applying the appropriate differentiation rules for each function composition or operation.
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