$\displaystyle X$has a beta distribution with p.d.f:

$\displaystyle f(x)=\left\{

\begin{array}{lr}

kx^2(1-x)^3&0\le x\le 1\\

0&otherwise

\end{array}

\right.$

First I had to find $\displaystyle k$ so I integrated for the interval $\displaystyle 0\le x\le 1$ and set it equal to $\displaystyle 1$ which gave $\displaystyle k=60$ . Correct?

But how do I find the mode? I can see from looking at the graph that it is $\displaystyle x=0.4$ , but how do I find it mathematically?