← OptimisationQuestion 1 of 16 · AS91578

A

A Christchurch irrigation channel has a rectangular cross-section. Its two sides and its base have a total length of 12 m, so with depth d m the width is 12 − 2d m and the cross-sectional area is A = d(12 − 2d) m².

Only your final answer is marked, not your working.

A(a) Find the depth that gives the greatest cross-sectional area. You may assume this gives a maximum.

A(b) Find the width of the channel at this depth.