Lösung 1.3:2b
Aus Online Mathematik Brückenkurs 2
In order to determine the function's extreme points, we investigate three types of points:
1. Critical points, i.e. where
x
=0
2. Points where the function is not differentiable;
3. Endpoints of the interval of definition.
In our case, we have that:
1. The derivative of
x
x
=3−2x
and becomes zero when
2. The function is a polynomial, and is therefore differentiable everywhere.
3. The function is defined for all
There is thus a point
If we write down a sign table for the derivative, we see that
TABLE
Because the function is given by a second-degree expression, its graph is a parabola with a maximum at
23
417
PICTURE TABLE