Stationary Points

What is a stationary point?

A stationary point on a curve where the gradient of the curve is zero. There are three types of stationary point: local maximum, local minimum and point of inflection. You can determine the type of stationary point by looking at the gradient of the curve on either side.

Example 1:

This is one method to distinguish between the stationary points. You can also use the second derivative in some cases:

Example 2:

You could be asked to determine the nature of stationary points of a function, in order to sketch a curve:

Example 3:

The following question below follows a format that has come up before numerous times. Try to go through the problem step by step to fully grasp the concept.

Practice Question:

Show Answer

Note: Here you can use either method so if you use the first derivative method, you won't lose the marks.