top of page ### 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.​ bottom of page