Mathematics - Differentiation Question with Solution | TestHub

Set $a=f\prime (1)$, $b=f^{\prime \prime }(1)$. The original equation at $x=1$ gives $b=a^2$. Differentiating and evaluating at 1 gives $2ab+8=3ab$, hence $ab=8$. Thus $a^3=8$, so $a=2$ and $b=4$.