Find the following using the table below. 1 2 3 4 1 3 2 4 4 2 f(x) f'(x) 13 g(x) 23 14 g'(x) 1 2 4 3 h' (2) if h(x) = f(x) · g(x) f(x) g(x) h' (2) if h(x) = f(g(x)) Question Help: h' (2) if h(x) = Video Message instructor
Find the following using the table below. 1 2 3 4 1 3 2 4 4 2 f(x) f'(x) 13 g(x) 23 14 g'(x) 1 2 4 3 h' (2) if h(x) = f(x) · g(x) f(x) g(x) h' (2) if h(x) = f(g(x)) Question Help: h' (2) if h(x) = Video Message instructor
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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Question
![**Problem Statement:**
Find the following using the table below.
**Table:**
| \( x \) | 1 | 2 | 3 | 4 |
|---------|---|---|---|---|
| \( f(x) \) | 1 | 3 | 3 | 4 |
| \( f'(x) \) | 1 | 3 | 4 | 2 |
| \( g(x) \) | 2 | 3 | 1 | 4 |
| \( g'(x) \) | 1 | 2 | 4 | 3 |
**Questions:**
1. \( h'(2) \) if \( h(x) = f(x) \cdot g(x) \)
[Answer Box]
2. \( h'(2) \) if \( h(x) = \frac{f(x)}{g(x)} \)
[Answer Box]
3. \( h'(2) \) if \( h(x) = f(g(x)) \)
[Answer Box]
**Question Help:**
- Video
- Message instructor
---
In the above table, the derivatives \( f'(x) \) and \( g'(x) \) are shown alongside functions \( f(x) \) and \( g(x) \) for the specified values of \( x \). The tasks require finding the derivative \( h'(2) \) for different compositions of functions \( f(x) \) and \( g(x) \) using the product, quotient, and chain rules.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b9a25ce-7950-429e-b571-3c0f034f6fd8%2F91154c11-2d63-495e-8d07-dcddf884dff7%2Ffa2jnti_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the following using the table below.
**Table:**
| \( x \) | 1 | 2 | 3 | 4 |
|---------|---|---|---|---|
| \( f(x) \) | 1 | 3 | 3 | 4 |
| \( f'(x) \) | 1 | 3 | 4 | 2 |
| \( g(x) \) | 2 | 3 | 1 | 4 |
| \( g'(x) \) | 1 | 2 | 4 | 3 |
**Questions:**
1. \( h'(2) \) if \( h(x) = f(x) \cdot g(x) \)
[Answer Box]
2. \( h'(2) \) if \( h(x) = \frac{f(x)}{g(x)} \)
[Answer Box]
3. \( h'(2) \) if \( h(x) = f(g(x)) \)
[Answer Box]
**Question Help:**
- Video
- Message instructor
---
In the above table, the derivatives \( f'(x) \) and \( g'(x) \) are shown alongside functions \( f(x) \) and \( g(x) \) for the specified values of \( x \). The tasks require finding the derivative \( h'(2) \) for different compositions of functions \( f(x) \) and \( g(x) \) using the product, quotient, and chain rules.
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