Find both turning points of a cubic

$y^{\prime}=6-6x-12x^2=-6(2x-1)(x+1)$, so $x=1/2$ or $x=-1$. Substitution gives $y(1/2)=11/4$ and $y(-1)=-4$.

$y^{\prime\prime}=-6-24x$. At $x=1/2$ this is $-18<0$, giving maximum $(1/2,11/4)$; at $x=-1$ it is $18>0$, giving minimum $(-1,-4)$. Both match the printed answers. These intermediate derivations are independently authored because neither copy supplies self-practice working.