Processing Math: Done
Lösung 1.3:2b
Aus Online Mathematik Brückenkurs 2
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<li>The derivative of <math>f(x)</math> is given by | <li>The derivative of <math>f(x)</math> is given by | ||
| - | {{ | + | {{Abgesetzte Formel||<math>f^{\,\prime}(x) = 3-2x</math>}} |
and becomes zero when <math>x=3/2\,</math>.</li> | and becomes zero when <math>x=3/2\,</math>.</li> | ||
Version vom 12:55, 10. 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
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Because the function is given by a second-degree expression, its graph is a parabola with a maximum at 2
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