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Math Help - [SOLVED] Critical Numbers

  1. #1
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    [SOLVED] Critical Numbers

    I need to find the critical numbers of the function f(x)=x(2-x)^2/5

    I found the derivative to be f'(x)= -(2/5)x (2-x)^(-3/5) + (2-x)^(2/5)

    But now I'm at a loss at how to factor the equation to find the values for x. Could someone give me a push in the right direction? Any help would be appreciated. Thanks!
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  2. #2
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    Quote Originally Posted by yzobel View Post
    I need to find the critical numbers of the function f(x)=x(2-x)^2/5

    I found the derivative to be f'(x)= -(2/5)x (2-x)^(-3/5) + (2-x)^(2/5)

    But now I'm at a loss at how to factor the equation to find the values for x. Could someone give me a push in the right direction? Any help would be appreciated. Thanks!
    Your derivative factorises as (2 - x)^{-3/5} \left( - \frac{2}{5} x + (2 - x)\right) ....
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