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Math Help - factoring/increasing decreasing functions

  1. #1
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    factoring/increasing decreasing functions

    I am in Increasing and Decreasing Functions.

    I'm just wondering how to factor this. The original question was y=1/x^2+1, and taking the derrivative i was left with y'=-2x/(x^2+1)^2.

    how do i factor the derrivative to get the x's?
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  2. #2
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    What do you mean?. You want to solve for x?. It's already factored.

    Do you want to set to 0 and solve for x?. If so, about the only value x can have is 0.
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  3. #3
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    yeah i want to set it to = zero, but its kind of confusing because its a fraction and im not used to that.
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  4. #4
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    Well, you can't have division by 0 so concentrate on the numerator.

    You have \frac{-2x}{(x^{2}+1)^{2}}=0

    So, -2x=0

    Solve for x.

    If you want to find inflection points, find y'', set to 0 and solve for x.

    y''=\frac{2(3x^{2}-1)}{(x^{2}+1)^{3}}

    To set this to 0 and solve, just solve 2(3x^{2}-1)=0
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