defined on the interval [-9.4247778, 1.45619445]. Enter points, such as inflection points in ascending order, i.e. smallest x values first. Rememer that you can enter "pi" for as part of your answer. A. f(x) is concave down on the region -9pi/4 to -3pi/4 B. A global minimum for this function occurs at 0 C. A local maximum for this function which is not a global maximum occurs at 0.5 ⠀ ⠀
defined on the interval [-9.4247778, 1.45619445]. Enter points, such as inflection points in ascending order, i.e. smallest x values first. Rememer that you can enter "pi" for as part of your answer. A. f(x) is concave down on the region -9pi/4 to -3pi/4 B. A global minimum for this function occurs at 0 C. A local maximum for this function which is not a global maximum occurs at 0.5 ⠀ ⠀
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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![### Understanding the Function \(f(x) = \sin^2(x/3)\)
**Interval Definition:**
The function \(f(x) = \sin^2(x/3)\) is defined on the interval \([-9.42477778, 1.45619445]\).
**Tasks:**
- Enter points such as inflection points in ascending order, i.e., smallest x values first.
- Remember that you can enter "pi" for \(\pi\) as part of your answer.
**Analysis of the Function:**
#### A. Concavity
\( f(x) \) is concave down on the region:
\[ -9\pi/4 \quad \text{to} \quad -3\pi/4 \]
#### B. Global Minimum
A global minimum for this function occurs at:
\[ 0 \]
#### C. Local Maximum
A local maximum for this function which is not a global maximum occurs at:
\[ 0.5 \]
#### D. Increasing Intervals
The function is increasing on:
\[ -3\pi \quad \text{to} \quad -1.5\pi \]
and
\[ 0 \quad \text{to} \quad 1.456 \]
### Diagrams and Graphs
(Explanation in Detail)
The visual details of graphs or diagrams of \( f(x) = \sin^2(x/3) \) are expected to show the behavior of the function within the given interval. We expect sinusoidal wave behavior squared, indicating values between 0 and 1:
1. **Concavity**: The diagram would show regions where the graph curves downwards, indicating concave down.
2. **Global Minimum**: The lowest point on the graph should be visibly at \( x=0 \).
3. **Local Maximum**: A peak that is not the highest point overall, occurring at \( x=0.5 \).
4. **Increasing Intervals**: Portions of the graph where the function is moving upwards.
These points help in deeply understanding where the function reaches specific behavioral landmarks without the visual aid of the graph or diagram but interpreting the textual data effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F276d7283-01d9-45ed-a762-7e45846115eb%2F034c209c-5267-4d45-9914-465c72a891c2%2Faq2xq0z_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding the Function \(f(x) = \sin^2(x/3)\)
**Interval Definition:**
The function \(f(x) = \sin^2(x/3)\) is defined on the interval \([-9.42477778, 1.45619445]\).
**Tasks:**
- Enter points such as inflection points in ascending order, i.e., smallest x values first.
- Remember that you can enter "pi" for \(\pi\) as part of your answer.
**Analysis of the Function:**
#### A. Concavity
\( f(x) \) is concave down on the region:
\[ -9\pi/4 \quad \text{to} \quad -3\pi/4 \]
#### B. Global Minimum
A global minimum for this function occurs at:
\[ 0 \]
#### C. Local Maximum
A local maximum for this function which is not a global maximum occurs at:
\[ 0.5 \]
#### D. Increasing Intervals
The function is increasing on:
\[ -3\pi \quad \text{to} \quad -1.5\pi \]
and
\[ 0 \quad \text{to} \quad 1.456 \]
### Diagrams and Graphs
(Explanation in Detail)
The visual details of graphs or diagrams of \( f(x) = \sin^2(x/3) \) are expected to show the behavior of the function within the given interval. We expect sinusoidal wave behavior squared, indicating values between 0 and 1:
1. **Concavity**: The diagram would show regions where the graph curves downwards, indicating concave down.
2. **Global Minimum**: The lowest point on the graph should be visibly at \( x=0 \).
3. **Local Maximum**: A peak that is not the highest point overall, occurring at \( x=0.5 \).
4. **Increasing Intervals**: Portions of the graph where the function is moving upwards.
These points help in deeply understanding where the function reaches specific behavioral landmarks without the visual aid of the graph or diagram but interpreting the textual data effectively.
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