Given the function こx (x+2)(x-2) yl"=-6x(x²-ax+4) (x+a)³ (X -1)³ 3. with 3 Complete the first deri vative Include all maximums and minimeims. Include all yntervals decreasing, on analysis. where is increasing constant.
Given the function こx (x+2)(x-2) yl"=-6x(x²-ax+4) (x+a)³ (X -1)³ 3. with 3 Complete the first deri vative Include all maximums and minimeims. Include all yntervals decreasing, on analysis. where is increasing constant.
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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![**Function Analysis**
Given the function:
\[ y = \frac{-x^3}{(x+2)(x-2)} \]
with the second derivative:
\[ y'' = \frac{-6x(x^2 - 2x + 4)}{(x+2)^3(x-1)^3} \]
**Task:**
Complete the first derivative analysis. Include all maximums and minimums. Include all intervals where \( y \) is increasing, decreasing, or constant.
---
In this exercise, you are tasked with analyzing the behavior of the given function by examining its derivatives. The goal is to determine the critical points (maximums and minimums) and to identify the intervals where the function is increasing or decreasing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3341284f-d761-40a1-94fb-8b0932aec828%2F404700d4-5e0b-4bfe-addb-2fdc19211c1e%2F08wsf4m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Function Analysis**
Given the function:
\[ y = \frac{-x^3}{(x+2)(x-2)} \]
with the second derivative:
\[ y'' = \frac{-6x(x^2 - 2x + 4)}{(x+2)^3(x-1)^3} \]
**Task:**
Complete the first derivative analysis. Include all maximums and minimums. Include all intervals where \( y \) is increasing, decreasing, or constant.
---
In this exercise, you are tasked with analyzing the behavior of the given function by examining its derivatives. The goal is to determine the critical points (maximums and minimums) and to identify the intervals where the function is increasing or decreasing.
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