Solution
= Solution
The <probability density function> is zero outside $[0,1]$. Inside that <interval>, it rises from $(0,0)$, reaches its only interior maximum at $x=2/3$, and falls to $(1,0)$. The <derivative> is
$$
f'(x)=12x(2-3x),
$$
positive for $0<x<2/3$ and negative for $2/3<x<1$. Its maximum height is $f(2/3)=16/9$. The second panel of the figure in part (b) shows the <function graph> on the requested full range, with this <mode> marked.