Clear[f, x];

\(f[x_]\  = \ x*\((12 - x)\)^2; 
Plot[f[x], {x, 0, 12}]; \)

Expand[f[x], x]

Integrate[f[x], {x, 0, 12}]

Solve[D[f[x], x] == 0, x]

f[4]