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
Find or approximate all points at which the given function equals its average value
![**Educational Content Transcription:**
---
### Theorem for Integrals
**Instruction:** Find or approximate all points where the function equals its average value on the given interval.
1. **Graph Analysis:**
A graph is displayed with the function \( y = 5(1 + \cos x) \), which shows one period of a cosine wave starting at \( \frac{-\pi}{2} \), peaking at 10, and ending at \( \pi \). The x-axis has markings at \( \frac{-\pi}{2} \), 0, and \( \pi \).
2. **Function and Interval:**
- **40.** \( f(x) = e^x \) on \([0, 2]\)
3. **Absolute Value Function:**
- **43.** \( f(x) = 1 - |x| \) on \([-1, 1]\)
**Task:** Determine if the following statement is correct with an explanation or counterexample:
- If the line \( x = 2 \), then...
(Continuation is missing, and additional information might be required to complete the exercise.)
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Transcribed Image Text:**Educational Content Transcription:**
---
### Theorem for Integrals
**Instruction:** Find or approximate all points where the function equals its average value on the given interval.
1. **Graph Analysis:**
A graph is displayed with the function \( y = 5(1 + \cos x) \), which shows one period of a cosine wave starting at \( \frac{-\pi}{2} \), peaking at 10, and ending at \( \pi \). The x-axis has markings at \( \frac{-\pi}{2} \), 0, and \( \pi \).
2. **Function and Interval:**
- **40.** \( f(x) = e^x \) on \([0, 2]\)
3. **Absolute Value Function:**
- **43.** \( f(x) = 1 - |x| \) on \([-1, 1]\)
**Task:** Determine if the following statement is correct with an explanation or counterexample:
- If the line \( x = 2 \), then...
(Continuation is missing, and additional information might be required to complete the exercise.)
---
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