Intervals of increase and the intervals of decrease?

AI Thread Summary
The function y=-(x-3)^5(x+1)^4 has a degree of 9 and a negative leading coefficient, indicating it will have end behaviors where y approaches infinity as x approaches negative infinity and y approaches negative infinity as x approaches positive infinity. The roots of the function are x=3 and x=-1, with a y-intercept of 243. To determine the intervals of increase and decrease, the derivative is typically used, as a positive derivative indicates an increasing function. Although derivatives have not been covered in the course, understanding that the function increases where the derivative is positive is crucial. Thus, identifying the intervals of increase and decrease will require analysis of the function's behavior around its critical points.
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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