**Function has absolute minimum= `-1/root(8)(e)` at x=-1**

`f(x)=xe^(-x^2/8)`

differentiating by applying product rule,

`f'(x)=x(e^(-x^2/8))((-2x)/8)+e^(-x^2/8)`

`f'(x)=e^(-x^2/8)(-x^2/4+1)`

`f'(x)=-1/4e^(-x^2/8)(x^2-4)`

Now to find the absolute extrema of the function , that is...

(The entire section contains 2 answers and 161 words.)

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