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Math Help - intervals of increase and the intervals of decrease?

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    10

    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?
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  2. #2
    Member
    Joined
    Mar 2009
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    Alberta
    Posts
    173
    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.

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