A rectangular box with a square base and no top must hold a fixed volume
MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
A rectangular box with a square base and no top must hold a fixed volume. A student models the outside surface area S as a differentiable function of the base edge length x and finds that S′(x0)=0 and S′′(x0)>0 at x=x0. Which statement best interprets these calculus results in the context of the design problem?
(a) The material required to build the box is maximized when the base edge length is x0.
(b) The material required to build the box is minimized when the base edge length is x0.
(c) The box’s volume is minimized when the base edge length is x0.
(d) Near x0, changing the base edge length does not change the surface area at all.