Lösung 1.3:1b

Aus Online Mathematik Brückenkurs 2

Version vom 10:08, 11. Mär. 2009

There are two points, x=a and x=b (see picture below), where the function has a horizontal tangent and hence a derivative equal to zero. These are the functions critical points.

Furthermore, we see that the function has local minimum points at the left endpoint of the interval of definition and x=b, because the function takes higher values at neighbouring points. In the same way, we see that the function has local maximum points at x=a and at the right endpoint of the interval of definition.

Of these local extreme points, the left endpoint is a global minimum (that point where the function takes its absolute minimum value) and the right endpoint is a global maximum.

The function is strictly increasing (it has a tangent that slopes upwards) in the interval between the left endpoint and x=a, as well as between x=b and the right endpoint. In the interval between x=0 and x=b, the function is strictly decreasing.