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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![### Problem Statement:
**Choose the correct distance traveled based on the given problem:**
**Problem**: Suppose \( s(t) = 8t - 2t^2 \) on the interval \([0, 4]\).
**Question**: What is the distance traveled on \([0, 4]\)?
**Options**:
1. \( \quad \ \mathbf{0} \)
2. \( \quad \ \mathbf{4} \)
3. \( \quad \ \mathbf{8} \)
4. \( \quad \mathbf{16} \)
### Additional Explanation:
In order to find the distance traveled on the interval \([0, 4]\), we need to consider the motion described by the position function \(s(t) = 8t - 2t^2\). We specifically need to understand how the position changes over time within the given interval. Calculations involving the derivative of the function can help us determine any changes in direction, which is essential for accurately computing the total distance traveled.
For an educational website, it would be useful to include a step-by-step detailed explanation and process of determining the distance, possibly with diagrams of the graph of \(s(t)\), and marking critical points of changes and intervals of increasing/decreasing behavior.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5fb4dfc3-db65-4bb6-9a5b-9427f46c7a3d%2F9d3ba92a-ef32-482f-ae8d-c0ef2fc83f6d%2Ftpl6d0j_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
**Choose the correct distance traveled based on the given problem:**
**Problem**: Suppose \( s(t) = 8t - 2t^2 \) on the interval \([0, 4]\).
**Question**: What is the distance traveled on \([0, 4]\)?
**Options**:
1. \( \quad \ \mathbf{0} \)
2. \( \quad \ \mathbf{4} \)
3. \( \quad \ \mathbf{8} \)
4. \( \quad \mathbf{16} \)
### Additional Explanation:
In order to find the distance traveled on the interval \([0, 4]\), we need to consider the motion described by the position function \(s(t) = 8t - 2t^2\). We specifically need to understand how the position changes over time within the given interval. Calculations involving the derivative of the function can help us determine any changes in direction, which is essential for accurately computing the total distance traveled.
For an educational website, it would be useful to include a step-by-step detailed explanation and process of determining the distance, possibly with diagrams of the graph of \(s(t)\), and marking critical points of changes and intervals of increasing/decreasing behavior.
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