Learn how to find stationary points and determine their nature

Finding stationary points, sometimes called local extrema, is one of the first applications of derivatives that students learn and is a very common exam question. The technique is quite straight-forward but is often overcomplicated by students and teachers. In particular, determining the nature of stationary points (i.e. what kind of stationary point) tends to cause more trouble than it needs to. Since stationary points are found using derivatives it’s crucial that you’re confident with that. Check out our videos on the Power Rule, the Product Rule, the Quotient Rule and the Chain Rule to review these techniques. In this video I discuss the theory you need for this technique and work a typical example problem. Any questions about this video drop us a message HERE.

Key Points

Stationary points occur where f ‘(x)=0

To find stationary points let f ‘(x)=0 and solve

The ‘nature’ of stationary points is what type they are

The three types are ‘maximum turning point’, ‘minimum turning point’, and ‘point of inflection’

To determine the nature of a stationary point use a nature table or the second derivative test

Stationary points also allow us to determine where a function is increasing or decreasing

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