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Math Help - Solve for x.

  1. #1
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    Solve for x.

    Given f(x) =(x)(e^(-x)), find x when f '''(x) - f ''(x)=0 I got solutions as x=0 & x= 3 and was wondering if that's the correct answer.
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  2. #2
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    Re: Solve for x.

    Quote Originally Posted by tenner View Post
    Given f(x) =(x)(e^(-x)), find x when f '''(x) - f ''(x)=0 I got solutions as x=0 & x= 3 and was wondering if that's the correct answer.
    f'''(x)=(3-x)\cdot e^{-x} ~\text { and }~ f''(x)=(x-2) \cdot e^{-x}

    Hence :

    f'''(x)-f''(x)=0

    (3-x)\cdot e^{-x}-(x-2) \cdot e^{-x}=0

    (5-2x)\cdot e^{-x}=0

    x=\frac{5}{2}
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