Aus Online Mathematik Brückenkurs 2
The function has critical points at the points
x=a
and
x=d, (see figure below), i.e. the derivatives are equal to zero, but note that
x=b
and
x=c
are not critical points (the derivative is not even defined at these points).
The function has local minimum points at
x=a,
x=c
and the right endpoint of the interval of definition and the local maximum points at the left endpoint,
x=b, and
x=d. Of these,
x=b
is the global maximum and
x=a
is the global minimum.
Between the local extreme points, the function is strictly increasing or decreasing.
