Intervals of increase and the intervals of decrease?

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SUMMARY

The function y=-(x-3)^5(x+1)^4 has a degree of 9 and a negative leading coefficient, indicating that it opens downwards. The roots are located at x=3 and x=-1, with a y-intercept of 243. To determine the intervals of increase and decrease, one must analyze the sign of the derivative, which is positive when the function is increasing and negative when it is decreasing. The end behavior shows that as x approaches negative infinity, y approaches positive infinity, and as x approaches positive infinity, y approaches negative infinity.

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  • Introduction to derivatives and their significance in determining function behavior
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  • Learn how to calculate the derivative of polynomial functions
  • Study the First Derivative Test for identifying intervals of increase and decrease
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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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