Aus Online Mathematik Brückenkurs 2

The function has critical points at the points \displaystyle x=a and \displaystyle x=d, (see figure below), i.e. the derivatives are equal to zero, but note that \displaystyle x=b and \displaystyle x=c are not critical points (the derivative is not even defined at these points).

The function has local minimum points at \displaystyle x=a, \displaystyle x=c and the right endpoint of the interval of definition and the local maximum points at the left endpoint, \displaystyle x=b, and \displaystyle x=d. Of these, \displaystyle x=b is the global maximum and \displaystyle x=a is the global minimum.

Between the local extreme points, the function is strictly increasing or decreasing.