Second Derivative and Stationary Points

To find the second derivative we apply the same method as , we just do it twice. This lets us find the rate of change for the rate of change. This can be represented as or

A positive second derivative means that the gradient is increasing, implying a minimum point. The opposite is also true, a negative second derivative means that the gradient is decreasing, implying a maximum point.

Inflection points are points on a curve at which the curvature changes sign. It is a point in which the concavity of the function changes. So at either side of a point of inflection, changes sign