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Math Help - How to find the critical point of this?

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    How to find the critical point of this?

    f(x)=x^(10)e^(−13x)

    The derivative is f(x)=(10x^(9)−13x^(10)) * e^ (−13x)
    The derivative is right because its given, I don't understand how solve for x = 0 correctly to find the critical points.. can someone direct me?
    I would have thought x = 0 and sqrt(10/13) but apparently i not correct.
    Last edited by mr fantastic; March 18th 2011 at 06:50 PM. Reason: Title.
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    The derivative factorises further to \displaystyle f'(x) = x^9(10 - 13x)e^{-13x}.

    Set this equal to \displaystyle 0 and solve for \displaystyle x using the null factor law.
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    Quote Originally Posted by ASUSpro View Post
    f(x)=x^(10)e^(−13x)

    The derivative is f(x)=(10x^(9)−13x^(10)) * e^ (−13x)
    The derivative is right because its given, I don't understand how solve for x = 0 correctly to find the critical points.. can someone direct me?
    I would have thought x = 0 and sqrt(10/13) but apparently i not correct.
    No, the derivative is f'(x)=(10x^(9)−13x^(10)) * e^ (−13x).

    You're expected to solve f'(x) = 0, that is, 10x^(9)−13x^(10) = 0.
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