Optimisation

Using calculus to find a maximum or minimum value. CAPS Grade 12 definition, worked NSC example and related calculus practice.

Using calculus to find a maximum or minimum value.

Definition

Optimisation uses differentiation to find the largest or smallest value of a quantity subject to a constraint. Write the constraint, substitute to get a single-variable function, then solve the derivative equal to zero.

Worked example

For a rectangle with perimeter 40 m, area A = x(20 − x) is maximised when A′ = 20 − 2x = 0, so x = 10 m (a square).

Where it appears in the exam

Paper 1 calculus includes an applied optimisation question on area, volume, cost or distance.

Step-by-step method

  1. Write the quantity to optimise in terms of the variables.
  2. Use the constraint to write it in one variable.
  3. Differentiate and set the derivative equal to zero.
  4. Solve, confirm it is a maximum or minimum, and answer in context with units.

Common mistake

Stopping at the x-value without answering the question that was asked.

Related calculus terms

Frequently asked questions

What does optimisation mean in Grade 12 Maths?

Optimisation uses differentiation to find the largest or smallest value of a quantity subject to a constraint. Write the constraint, substitute to get a single-variable function, then solve the derivative equal to zero.

Which NSC paper tests optimisation?

Optimisation belongs to the Calculus section of CAPS Grade 12 Mathematics, which is examined in Paper 1.

How do I practise questions involving optimisation?

Snap a question that uses optimisation into the Snap&Learn AI solver, or work through the calculus topic guide and NSC past papers.

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