Given the function y"=-6X(x²-ax+4) (x+a)³ (x -1)³ 3. with (X+2)(x-) - analysiS Enclude all maximums and minimems. increa Complete the first deri vative luda entervals where y is
Given the function y"=-6X(x²-ax+4) (x+a)³ (x -1)³ 3. with (X+2)(x-) - analysiS Enclude all maximums and minimems. increa Complete the first deri vative luda entervals where y is
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
I’ve asked this once but I think part of the answer was written wrong.
![**Transcription for Educational Website:**
---
**Given Function for Analysis**
Consider the function:
\[ y = \frac{-x^3}{(x+2)(x-2)} \]
The second derivative of the function is given by:
\[ y'' = \frac{-6x(x^2 - 2x + 4)}{(x+2)^3(x-1)^3} \]
---
**Task: First Derivative Analysis**
1. **Complete the First Derivative Analysis:**
- Determine the critical points where the first derivative equals zero or is undefined.
- Identify and classify any local maxima or minima based on these critical points.
2. **Intervals of Behavior:**
- Analyze and record all intervals where the function \( y \) is increasing, decreasing, or constant.
This exercise encourages understanding of calculus concepts such as derivatives, critical point analysis, and function behavior analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3341284f-d761-40a1-94fb-8b0932aec828%2Fb947ee6d-42e7-40de-ab3e-846170452c75%2Fyezxfon_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website:**
---
**Given Function for Analysis**
Consider the function:
\[ y = \frac{-x^3}{(x+2)(x-2)} \]
The second derivative of the function is given by:
\[ y'' = \frac{-6x(x^2 - 2x + 4)}{(x+2)^3(x-1)^3} \]
---
**Task: First Derivative Analysis**
1. **Complete the First Derivative Analysis:**
- Determine the critical points where the first derivative equals zero or is undefined.
- Identify and classify any local maxima or minima based on these critical points.
2. **Intervals of Behavior:**
- Analyze and record all intervals where the function \( y \) is increasing, decreasing, or constant.
This exercise encourages understanding of calculus concepts such as derivatives, critical point analysis, and function behavior analysis.
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