Prove that if $p > 0$, then there exists a constant $C_p$ such that for $x > 0$,
$\hspace{5cm}$ $x^p$ $\leq$ $C_pe^x$
The book gave a hint: examine the derivative of $\hspace{.1cm}$ $x^pe^{-x}$
This problem is in the Mean Value Theorem chapter in our book. I really have no idea where to start or what part of the MVT to use.