2 3 Perform a first derivative test on the function f(x) = x (x-2); [-2,2]. a. Locate the critical points of the given function. b. Use the First Derivative Test to locate the local maximum and minimum values. c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist). A. There is a local minimum at x = 4 5 (Type an integer or a simplified fraction.) B. There is no local minimum. c. Identify the absolute maximum value. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute maximum value is 0. (Type an integer or a decimal rounded to two decimal places as needed.) B. There is no absolute maximum. Identify the absolute minimum value. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute minimum value is -6.35. (Type an integer or a decimal rounded to two decimal places as needed.) B. There is no absolute minimum.
2 3 Perform a first derivative test on the function f(x) = x (x-2); [-2,2]. a. Locate the critical points of the given function. b. Use the First Derivative Test to locate the local maximum and minimum values. c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist). A. There is a local minimum at x = 4 5 (Type an integer or a simplified fraction.) B. There is no local minimum. c. Identify the absolute maximum value. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute maximum value is 0. (Type an integer or a decimal rounded to two decimal places as needed.) B. There is no absolute maximum. Identify the absolute minimum value. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute minimum value is -6.35. (Type an integer or a decimal rounded to two decimal places as needed.) B. There is no absolute minimum.
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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![### First Derivative Test on the Function
Perform a first derivative test on the function \( f(x) = x^{\frac{2}{3}}(x - 2) \), over the interval \([-2, 2]\).
#### Steps:
a. **Locate the critical points of the given function.**
b. **Use the First Derivative Test to locate the local maximum and minimum values.**
c. **Identify the absolute maximum and minimum values of the function on the given interval (when they exist).**
### Answers:
#### a. Locate the Critical Points
- The chosen point shows there is a local minimum at \( x = \frac{4}{5} \).
#### c. Absolute Maximum Value
- **Option A (Correct):** The absolute maximum value is \( 0 \).
#### Absolute Minimum Value
- **Option A (Correct):** The absolute minimum value is \( -6.35 \).
Note: For each calculation, ensure to fill in the answer boxes with integers or decimals rounded to two decimal places as needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60e5fca3-b9c2-47c4-9eba-5478d8641133%2F9e1109b9-6a35-4d8b-bedf-f6e31d2576ee%2Fpqmwo7i_processed.png&w=3840&q=75)
Transcribed Image Text:### First Derivative Test on the Function
Perform a first derivative test on the function \( f(x) = x^{\frac{2}{3}}(x - 2) \), over the interval \([-2, 2]\).
#### Steps:
a. **Locate the critical points of the given function.**
b. **Use the First Derivative Test to locate the local maximum and minimum values.**
c. **Identify the absolute maximum and minimum values of the function on the given interval (when they exist).**
### Answers:
#### a. Locate the Critical Points
- The chosen point shows there is a local minimum at \( x = \frac{4}{5} \).
#### c. Absolute Maximum Value
- **Option A (Correct):** The absolute maximum value is \( 0 \).
#### Absolute Minimum Value
- **Option A (Correct):** The absolute minimum value is \( -6.35 \).
Note: For each calculation, ensure to fill in the answer boxes with integers or decimals rounded to two decimal places as needed.
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