### 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.

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###### 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.

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###### 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.