IB skill practice

Solve optimization problems

Model and solve maximum or minimum problems using derivatives and clear interpretation.

Paper 1 6 marks Difficulty 3

Maximise an area model

A rectangular pen has perimeter \(60\) m. Let width be \(x\), so \(A(x)=30x-x^{2}\). Find optimal width, length, and maximum area.

Worked practice: optimization

Find the dimensions at the vertex, then state the maximum area.