Applications of Differentiation

Types of Turning Points

This page will explore the minimum and maximum turning points and how to determine them using the sign test.​

The Sign Test

The sign test is where you determine the gradient on the left and on the right side of the stationary point to determine its nature.

Minimum Turning Point

A  minimum turning point is a stationary point that has a gradient of 0 and has a negative gradient on the left side of the stationary point and a positive gradient on the right side of the stationary point. 

 

We can use the sign test to prove (0,0) is a minimum turning point in the graph y=x^2.

As the left side of the stationary point is a negative gradient, and the right side produces a positive gradient, the stationary point is a minimum turning point.

Maximum Turning Point​

A maximum turning point is a point that has a 0 gradient, the left side has a positive gradient and the right side has a negative gradient.

We can use the sign test to prove (0,2) is a maximum turning point on the graph y=-x^2 +2.​