g(t) g'(t) h(t) h'(t) -10 6. -1 -9 1 -3 1 -3 5 2 4 14 -1 -1/4 3 2 -1.5 -2 4 8 1/2 1 find: f '(1) find: f'(4) find: f (0) find: f'(2) 5. Given f(t) = g(t)· h(t)
g(t) g'(t) h(t) h'(t) -10 6. -1 -9 1 -3 1 -3 5 2 4 14 -1 -1/4 3 2 -1.5 -2 4 8 1/2 1 find: f '(1) find: f'(4) find: f (0) find: f'(2) 5. Given f(t) = g(t)· h(t)
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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![Certainly! Below is a transcription and detailed explanation suitable for an educational website.
---
### Table of Functions and Derivatives
This table presents the values of two functions, \( g(t) \) and \( h(t) \), along with their derivatives \( g'(t) \) and \( h'(t) \) evaluated at different points \( t \).
| \( t \) | \( g(t) \) | \( g'(t) \) | \( h(t) \) | \( h'(t) \) |
|---------|------------|-------------|------------|-------------|
| 0 | -10 | 6 | -1 | -9 |
| 1 | -3 | 1 | -3 | 5 |
| 2 | 4 | 14 | -1 | -1/4 |
| 3 | 2 | -1.5 | -2 | 5 |
| 4 | 0 | 8 | 1/2 | 1 |
### Problem 5 Instructions
Given the function \( f(t) = g(t) \cdot h(t) \), determine the derivative \( f'(t) \) at various points. To find \( f'(t) \), use the product rule for derivatives, which states:
\[ f'(t) = g'(t) \cdot h(t) + g(t) \cdot h'(t) \]
#### Derivative Calculations
Calculate \( f'(t) \) at the following points:
- **Find \( f'(1) \):**
- **Find \( f'(4) \):**
- **Find \( f'(0) \):**
- **Find \( f'(2) \):**
---
This transcription provides a structured understanding of the data and instructions necessary to apply the product rule to compute derivatives at specified points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9db5004-41b4-46a8-9c5d-150bc716e4bd%2F40f2c070-df79-485c-91be-c96650dca10c%2F4hg1cvc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Below is a transcription and detailed explanation suitable for an educational website.
---
### Table of Functions and Derivatives
This table presents the values of two functions, \( g(t) \) and \( h(t) \), along with their derivatives \( g'(t) \) and \( h'(t) \) evaluated at different points \( t \).
| \( t \) | \( g(t) \) | \( g'(t) \) | \( h(t) \) | \( h'(t) \) |
|---------|------------|-------------|------------|-------------|
| 0 | -10 | 6 | -1 | -9 |
| 1 | -3 | 1 | -3 | 5 |
| 2 | 4 | 14 | -1 | -1/4 |
| 3 | 2 | -1.5 | -2 | 5 |
| 4 | 0 | 8 | 1/2 | 1 |
### Problem 5 Instructions
Given the function \( f(t) = g(t) \cdot h(t) \), determine the derivative \( f'(t) \) at various points. To find \( f'(t) \), use the product rule for derivatives, which states:
\[ f'(t) = g'(t) \cdot h(t) + g(t) \cdot h'(t) \]
#### Derivative Calculations
Calculate \( f'(t) \) at the following points:
- **Find \( f'(1) \):**
- **Find \( f'(4) \):**
- **Find \( f'(0) \):**
- **Find \( f'(2) \):**
---
This transcription provides a structured understanding of the data and instructions necessary to apply the product rule to compute derivatives at specified points.
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