Use the Second Derivative Test to find the location of all local extrema in the interval (-2, 8) for the function given below. Provide your answer below: f(x) = 3 If there is more than one local maxima or local minima, write each value of x separated by a comma. If a local maxima or local minima does not occur on the function, enter Ø in the appropriate box. Answer should be exact. The local maxima occur at x = 2x² + 3x The local minima occur at x =
Use the Second Derivative Test to find the location of all local extrema in the interval (-2, 8) for the function given below. Provide your answer below: f(x) = 3 If there is more than one local maxima or local minima, write each value of x separated by a comma. If a local maxima or local minima does not occur on the function, enter Ø in the appropriate box. Answer should be exact. The local maxima occur at x = 2x² + 3x The local minima occur at x =
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 36E
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![### Educational Content: Finding Local Extrema Using the Second Derivative Test
#### Problem Statement:
**Objective:** Use the Second Derivative Test to find the location of all local extrema in the interval (-2, 8) for the function given below.
\[ f(x) = \frac{x^3}{3} - 2x^2 + 3x \]
**Instructions:**
1. Identify the values of \( x \) where there are local maxima or local minima in the given interval.
2. If there is more than one local maxima or local minima, write each value of \(x\) separated by a comma.
3. If no local maxima or local minima occur on the function, enter \(\emptyset\) in the appropriate box.
**Note:** Answers should be exact.
#### Response Section:
Provide your answer below:
- **The local maxima occur at \( x = \text{__________} \).**
- **The local minima occur at \( x = \text{__________} \).**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5032fc1e-2501-46ab-88b4-e27880dbbd0e%2F6d00d387-8bc9-45be-80cc-25deae826a7f%2Fvzhwor_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Content: Finding Local Extrema Using the Second Derivative Test
#### Problem Statement:
**Objective:** Use the Second Derivative Test to find the location of all local extrema in the interval (-2, 8) for the function given below.
\[ f(x) = \frac{x^3}{3} - 2x^2 + 3x \]
**Instructions:**
1. Identify the values of \( x \) where there are local maxima or local minima in the given interval.
2. If there is more than one local maxima or local minima, write each value of \(x\) separated by a comma.
3. If no local maxima or local minima occur on the function, enter \(\emptyset\) in the appropriate box.
**Note:** Answers should be exact.
#### Response Section:
Provide your answer below:
- **The local maxima occur at \( x = \text{__________} \).**
- **The local minima occur at \( x = \text{__________} \).**
![### Second Derivative Test for Local Extrema
#### Problem Statement
Use the Second Derivative Test to find the location of all local extrema in the interval \((-2, 8)\) for the function given below:
\[ f(x) = \frac{x^3}{3} - 2x^2 + 3x \]
If there is more than one local maxima or local minima, write each value of \( x \) separated by a comma. If a local maxima or local minima does not occur on the function, enter ∅ in the appropriate box. The answer should be exact.
#### Input Fields
Provide your answer below:
- **Local Maxima**: The local maxima occur at \( x = \) [________].
- **Local Minima**: The local minima occur at \( x = \) [________].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5032fc1e-2501-46ab-88b4-e27880dbbd0e%2F6d00d387-8bc9-45be-80cc-25deae826a7f%2Fqbzhzdr_processed.png&w=3840&q=75)
Transcribed Image Text:### Second Derivative Test for Local Extrema
#### Problem Statement
Use the Second Derivative Test to find the location of all local extrema in the interval \((-2, 8)\) for the function given below:
\[ f(x) = \frac{x^3}{3} - 2x^2 + 3x \]
If there is more than one local maxima or local minima, write each value of \( x \) separated by a comma. If a local maxima or local minima does not occur on the function, enter ∅ in the appropriate box. The answer should be exact.
#### Input Fields
Provide your answer below:
- **Local Maxima**: The local maxima occur at \( x = \) [________].
- **Local Minima**: The local minima occur at \( x = \) [________].
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