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Math Help - For each of the following intervals, state whether the function is positive or Negati

  1. #1
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    For each of the following intervals, state whether the function is positive or Negati

    f(x)= (3-x)(5+x)/x(x+3)^2

    x<-5 pos or neg?
    -5<x<-3 pos or neg?
    -3<x<0 pos or neg
    0<x<3 pos or neg
    x>3 pos or neg

    The zeros of the eq are, 3 , -5, 0, and -3. But after that, I have no idea how to finish the question.):
    Help would be much appreciated!
    Thnx~
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  2. #2
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    The zeroes of an equation are where it literally is equal to zero. The zeroes that make an equation undefined are not the same. There are all however critical points.

    With these critical points, just test points IN BETWEEN. . .this will give you the behavior of the function in those intervals.
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  3. #3
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    ANDS! method works fine. You can also do this by remembering that the product of an even number of negative numbers is positive, and the product of an odd number of negative numbers is negative. Just count the number of negative factors. Notice that, except at x= -3, as you pass from one interval to the next, exactly one factor changes sign. We have to except x=-3 because (x+3) is squared so that will always count as two factors.
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