What are the critical values, if any, of $f (x) = x e^{2 x}$ $f(x) = xe^(2x)$ ?

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Answer 1 · 2017-04-13T02:35:53

Critical Value: $x = - \frac{1}{2}$ $x=-1/2$

$f (x) = x e^{2 x}$ $f(x)=xe^(2x)$

$f'(x)=1 cdot e^(2x)+x cdot 2e^(2x)=(1+2x)e^(2x)$

By setting $f'(x)=0$ ,

$(1+2x)e^(2x)=0$

By dividing both sides by $e^(2x)$ ,

$1+2x=0$

By subtracting 1 from both sides,

$2x=-1$

By dividing both sides by $2$ ,

$x=-1/2$ (Critical Value)

I hope that this was clear.

What are the critical values, if any, of f(x) = xe^(2x)f(x)=xe2xf(x) = xe^(2x)?