derivative of a cubic function
The derivative of a cubic function is a quadratic function. A critical point is a point where the tangent is parallel to the x-axis, it is to say, that the slope of the tangent line at that point is zero. In the following example we can see a cubic function with two critical points. One is a local maximum and the other is a local minimum. In these points, the derivative function (a parabola) cut the x-axis: