Question
Given the function $f(x)=x^{2} e^{-2 x}, x>0 .$ Then $f(x)$ has the maximum value equal to(a) $e^{-t}$(b) $(2 e)^{-1}$(c) $e^{-2}$(d) none of these
Step 1
The function is $f(x)=x^{2} e^{-2 x}$, so by using the product rule and chain rule, we get \[f'(x) = 2x e^{-2x} - 2x^{2} e^{-2x} = 2x(1-x) e^{-2x}.\] Show more…
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