Optimisation

Optimisation problems ask for a maximum or minimum value in context.

1. Define variables clearly.
2. Build a single-variable model.
3. Differentiate.
4. Solve \(f'(x)=0\).
5. Check the result and answer in context.

Example structure

If an area is given by \(A(x)=x(20-2x)\), then

\[A'(x)=20-4x.\]

Solving \(A'(x)=0\) gives \(x=5\).