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`f(x) = x e^(-x^2/8), [-1, 4]` Find the absolute maximum and minimum values of f on the given interval

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

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gsarora17 eNotes educator | Certified Educator

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write762 answers

starTop subjects are Math, Science, and Business

`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 continuous on a closed interval, we...

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