The function \( f(x) \) defined for all real numbers \( \mathrm{x} \) has the following properti...

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The function \( f(x) \) defined for all real numbers \( \mathrm{x} \) has the following properties
\( f^{\prime}(x)=k\left(2 x-x^{2}\right) e^{-x} \) for some constant \( k0 \). Find
(a) The intervals on which \( f \) is increasing and decreasing and any local maximum or minimum values.
(b) The intervals on which the graph \( f \) is concave down and concave up.
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