Solution
= Solution
The interior <stationary point> of the <probability density function> solves $12x(2-3x)=0$ with $0<x<1$, giving $x=2/3$. The sign change of $f'$ established in part (d), together with zero endpoint values, makes this the global maximum. Thus
$$
\boxed{\text{mode}=\frac23,\qquad f(2/3)=\frac{16}{9}.}
$$