Modelling with Differentiation inc. Optimisation (Edexcel A-Level Mathematics): Flashcards

It represents the rate of change of a function.

Points where the derivative is zero or undefined.

If $> 0$ it's a minimum, $< 0$ it's a maximum, $= 0$ is inconclusive.

To find maximum or minimum values of a function.

Define the problem clearly and identify variables.

It represents the quantity to maximize or minimize.

Solve $f'(x) = 0$ and check undefined points.

Optimizing profit, cost, revenue, or utility functions.

$A = \text{length} \times \text{width}$, often subject to constraints.

It represents the highest value in a small neighborhood.