Solve for x.

**tenner** · April 11th 2012, 09:13 PM

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.

**princeps** · April 11th 2012, 09:41 PM

Originally Posted by tenner

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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Solve for x.

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