Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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**Calculus Problem: Estimating Change Using Derivatives**

**Problem Statement:**

Suppose the following values of \( f'(t) \) are known:

| \( t \) | \( f'(t) \) |
|---------|-------------|
| 0       | 4           |
| 1       | 6           |
| 2       | 2           |
| 3       | 1           |

Use these values to estimate the change in \( f(t) \) between 0 and 1. Calculate \( f(1) - f(0) \).

**Instructions:**

1. Review the given values of the derivative \( f'(t) \) at discrete points \( t = 0, 1, 2, \text{and } 3 \).

2. Estimate the change in function values over the interval \([0, 1]\) using the appropriate derivative value.

3. Enter your estimated result for \( f(1) - f(0) \) in the designated box.

**Note:**

- Your progress will be auto-saved, and if not submitted, the saved work will be auto-submitted on the due date.

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Transcribed Image Text:--- **Calculus Problem: Estimating Change Using Derivatives** **Problem Statement:** Suppose the following values of \( f'(t) \) are known: | \( t \) | \( f'(t) \) | |---------|-------------| | 0 | 4 | | 1 | 6 | | 2 | 2 | | 3 | 1 | Use these values to estimate the change in \( f(t) \) between 0 and 1. Calculate \( f(1) - f(0) \). **Instructions:** 1. Review the given values of the derivative \( f'(t) \) at discrete points \( t = 0, 1, 2, \text{and } 3 \). 2. Estimate the change in function values over the interval \([0, 1]\) using the appropriate derivative value. 3. Enter your estimated result for \( f(1) - f(0) \) in the designated box. **Note:** - Your progress will be auto-saved, and if not submitted, the saved work will be auto-submitted on the due date. ---
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