intervals of increase and the intervals of decrease?

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?

Start by differentiating the function. Keep in mind that a positive first derivative tells us that the function is increasing at a point, and that a negative derivative tells us that the function is decreasing.

Thus, you need to differentiate, find critical values (Values that cause the derivative to be undefined or 0, generally where a function changes from increasing to decreasing). Once you do this, pick test values from both sides of each critical value, if the derivative is + in an interval, the function is increasing in that interval. Likewise for a - derivative.

I hope this video helps, I used this guy's resources quite a bit.

http://www.youtube.com/watch?v=-W4d0qFzyQY