Thread: university engineering exam paper question on surface area of a box

a box with no lid has base rectangle of sides x,y and volume of the box is 9

i have shown that the surface area, S, is given by

S=xy+(18/x)+(18/y)

now i have to find the values of x and y such that S is a minimum but not sure where to start.

Well, start by finding the critical points of S.
Those points are the solutions of the equations & .

that is how i would do it, but the paper is foundation engineering maths and this has not been taught yet.

doing the Sx= Sy=0 leads to x=y. can this be deduced without resorting to partial diff?