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 Let $f(x)=x^a(1-x)^b$ where $a$ and $b$ are any two positive numbers.  Use $f$ in parts (a)-(d).
\begin{enumerate}[(a)]
\item If $a = 3$ and $b = 6$, find the absolute maximum value and the absolute minimum value of $f$ on $[0, 1]$.
\item If $a = 9$ and $b = 4$, find the absolute maximum value and the absolute minimum value of $f$ on $[0, 1]$.
\item If $a = \frac{2}{3}$ and $b = \frac{1}{4}$, find the absolute maximum value and the absolute minimum value of $f$ on $[0, 1]$.
\item If $a$ and $b$ are any positive numbers, find the absolute maximum and the absolute minimum value of $f$ on $[0,1]$.  Be sure you justify your conclusions.

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