A solid rectangular block is built with a square base of side $x$ cm. Its height is $h$ cm, and the block’s total surface area is $96\text{ cm}^2$.
(i)[3]
Express $h$ as a function of $x$ and show that the volume $V\text{ cm}^3$, of the block is $V = 24x - \tfrac{1}{2}x^3$.
(ii)[3]
Find the stationary value attained by $V$.
(iii)[2]
Determine whether this stationary value represents a maximum or a minimum.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Form an expression for the height, $h=\frac{24}{x}-\frac{x}{2}$.” …