CAIE P1 2010 June — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2010
SessionJune
TopicChain Rule

8 A solid rectangular block has a square base of side \(x \mathrm {~cm}\). The height of the block is \(h \mathrm {~cm}\) and the total surface area of the block is \(96 \mathrm {~cm} ^ { 2 }\).
  1. Express \(h\) in terms of \(x\) and show that the volume, \(V \mathrm {~cm} ^ { 3 }\), of the block is given by $$V = 24 x - \frac { 1 } { 2 } x ^ { 3 }$$ Given that \(x\) can vary,
  2. find the stationary value of \(V\),
  3. determine whether this stationary value is a maximum or a minimum.