Quick answer: Write the quantity to maximise or minimise as a function of one variable, solve f′(x) = 0, check that it is a maximum or a minimum, then answer the question asked, with units.
1) Write down what to maximise/minimise. 2) Express in one variable. 3) Differentiate + set = 0. 4) Verify it's a max not a min. Every SL AI optimisation question follows this frame.
Practise Optimisation — the 4-step method with AI marking
Open the full SL AI engine — every question in this unit is worked through with instant AI-graded feedback on your handwritten workings.
Use the constraint (a fixed perimeter, area or amount of material) to write the quantity in one variable, and state its domain.
Differentiate and solve f′(x) = 0. In AI you may solve it on the GDC, or read the maximum from the graph, unless the question says 'use calculus' or 'show that'.
Justify the type of turning point: the sign of f′ either side, f″(x), or the graph on the GDC. Check the ends of the domain too.
Answer the question asked: the dimension, the maximum value or both, with units.
Worked example
An open box is made from a 30 cm by 30 cm square of card by cutting a square of side x cm from each corner and folding up the sides. Find the value of x that gives the largest volume, and that volume.
Yes, unless the question says to use calculus or to show a result. Graph the function and use the maximum or minimum tool, but still write down the function you graphed.
Where can I practise optimisation questions?
On the Optimisation questions page: 15 exam-style SL AI questions with full mark schemes, plus free step-by-step worked examples.
Can I use my calculator for optimisation?
Yes: a GDC is allowed on every SL AI paper, so practise the calculator method as well as the working. The Graphs: intersections, zeros, max and min guide gives the keystrokes for the TI-84 Plus CE, TI-Nspire CX II and Casio fx-CG50.