Processing Math: Done
Lösung 1.3:2b
Aus Online Mathematik Brückenkurs 2
(Unterschied zwischen Versionen)
K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)) |
K (Solution 1.3:2b moved to Lösung 1.3:2b: Robot: moved page) |
Version vom 10:09, 11. Mär. 2009
In order to determine the function's extreme points, we investigate three types of points,
- critical points, i.e. where
f ,
(x)=0 - points where the function is not differentiable, and
- endpoints of the interval of definition.
In our case, we have that:
- The derivative of
f(x) is given by
and becomes zero whenf (x)=3−2xx=3 .
2 - The function is a polynomial, and is therefore differentiable everywhere.
- The function is defined for all x, and therefore the interval of definition has no endpoints.
There is thus just one point 2
If we write down a sign table for the derivative, we see that 2
| | | ||
| (x) | | | |
| |  | |  |
Because the function is given by a second-degree expression, its graph is a parabola with a maximum at 2
174)
