Intervals of increase and the intervals of decrease?

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Homework Help Overview

The discussion centers around the function y=-(x-3)^5(x+1)^4, specifically focusing on identifying the intervals of increase and decrease. The subject area involves polynomial functions and their behavior, particularly in relation to calculus concepts, despite the participants not having formal calculus training.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to analyze the function's characteristics, including its degree, roots, and end behaviors, while seeking guidance on determining intervals of increase and decrease without using derivatives. Some participants question the relationship between the derivative and the function's behavior, specifically regarding when the function is increasing.

Discussion Status

Participants are exploring the concept of derivatives in relation to function behavior. There is an acknowledgment that understanding when the derivative is positive can help identify intervals of increase, although the original poster expresses concern about not having learned calculus yet. Guidance has been offered regarding the significance of the derivative.

Contextual Notes

The original poster notes that they have not yet learned about derivatives, which may limit their ability to apply this concept directly to the problem at hand.

BuffaloSoulja
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y=-(x-3)^5(x+1)^4

For this function currently i have:

degree: 9
sign: negative ?
quadrants: I, II and 4
Roots: x=3 and -1
y-intercept= 243
domain: x belongs to E
range: y belongs to E
INTERVALS of INCREASE : ?
INTERVALS of DECREASE : ?
End Behaviors: As x approaches -infinity, y approaches infinity
as x approaches infinity, y approaches -infinity.


For the function y=-(x-3)^5(x+1)^4 what are the intervals of increase and the intervals of decrease?

I have been told to use derivatives. However, this isn't a calculus course and we haven't learned this yet
 
Physics news on Phys.org
What is true about the derivative when the function is increasing?
 
It is positive?
 
Yes. Find out when the derivative is positive, and you will have half of your answer.
 

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