Optimisation

This lesson covers optimisation — using differentiation to find maximum and minimum values in practical contexts — as required by the Edexcel A-Level Mathematics specification (9MA0). You need to be able to set up equations from word problems, differentiate, find stationary points, and verify their nature.

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What Is Optimisation?

Optimisation means finding the maximum or minimum value of a quantity. In A-Level Mathematics, this typically involves:

1. Setting up a function to be optimised (e.g., area, volume, cost, distance).
2. Writing the function in terms of one variable (using constraints to eliminate others).
3. Differentiating and setting dy/dx = 0 to find stationary points.
4. Using the second derivative (or other method) to verify the nature.
5. Answering the question in context.

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Step-by-Step Strategy