Classifying Stationary Points (Edexcel IGCSE Maths A (Modular))

Classifying Stationary Points

What are the different types of stationary points?

• You need to know two different types of stationary points:

  • Maximum points (this is where the graph reaches a “peak”)

  • Minimum points (this is where the graph reaches a “trough”)

    • These are also called turning points

    • Deciding which is which is called classifying them (or finding the nature of them)

• If a graph has multiple turning points, the one you are interested in can be described as a local maximum or minimum point

  • Other parts of the graph may still reach higher/lower values elsewhere

How do I classify turning points using graphs?

• You can use the shape of common graphs to classify different turning points

• To classify the turning point on a quadratic curve (parabola), remember that:

  • A positive quadratic (positive x² term) must have a minimum point

  • A negative quadratic (negative x² term) must have a maximum point

• To classify two different turning points on a cubic curve, remember that:

  • A positive cubic has a maximum point on the left and a minimum on the right

  • A negative cubic has a minimum point on the left and a maximum on the right