Maxima, Minima and Optimization

Start with derivatives

Maxima, Minima and Optimization is a section of Differentiation and Derivatives in Mathematics. The resources bring together questions about derivatives, local maxima and minima, stationary points and optimization. They give university students and school students a choice of formats for working through the topic, while teachers can open the materials for use with their students.

For a starting point, open the Differentiation flashcards. They ask about differentiation, notation and the gradient of a tangent. Then move to Nature of the Derivative, which asks about the second derivative, gradients and local minima.

Connect maps with questions

The mind map on maxima and minima includes local maxima and minima. Use it to organize the terms after working through the flashcards. The Calculus mind map also covers extrema of a function of a single variable, concavity, the second derivative test and geometric optimization.

Next, open Differentiation Nature questions. Its slides ask you to find stationary points and determine their nature. Work through a question, then return to the maps to check the ideas you used. You can use the same approach with a quiz: try the questions first, then return to a map or flashcard deck for the terms you want to study again.

Apply the ideas

The quiz on absolute maximum and minimum includes a question about a shape made from a cylinder and a hemisphere. A mind map also sets out steps for an assigned problem involving a manufacturer's revenue. These offer ways to look at optimization questions alongside the derivative and stationary-point resources.

Within Differentiation and Derivatives, the flashcards, maps and questions let you move between derivative notation and the maxima and minima covered on this page. Choose a map to study alongside a quiz.