Lösung 1.3:1d

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The function has critical points at the points
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<center> [[Image:1_3_1d-1(2).gif]] </center>
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<math>x=a</math>
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and
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<math>x=d</math>, (see figure below), i.e. the derivatives are equal to zero, but note that
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<center> [[Image:1_3_1d-2(2).gif]] </center>
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<math>x=b</math>
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and
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<math>x=c</math>
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are not critical points (the derivative is not even defined at these points).
[[Image:1_3_1_d1.gif|center]]
[[Image:1_3_1_d1.gif|center]]
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The function has local minimum points at
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<math>x=a</math>,
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<math>x=c</math>
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and the right endpoint of the interval of definition and the local maximum points at the left endpoint,
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<math>x=b</math>, and
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<math>x=d</math>. Of these,
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<math>x=b</math>
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is the global maximum and
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<math>x=a</math>
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is the global minimum.
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Between the local extreme points, the function is strictly increasing or decreasing.
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[[Image:1_3_1_d2.gif|center]]
[[Image:1_3_1_d2.gif|center]]

Version vom 09:29, 15. Okt. 2008

The function has critical points at the points \displaystyle x=a and \displaystyle x=d, (see figure below), i.e. the derivatives are equal to zero, but note that \displaystyle x=b and \displaystyle x=c are not critical points (the derivative is not even defined at these points).

The function has local minimum points at \displaystyle x=a, \displaystyle x=c and the right endpoint of the interval of definition and the local maximum points at the left endpoint, \displaystyle x=b, and \displaystyle x=d. Of these, \displaystyle x=b is the global maximum and \displaystyle x=a is the global minimum.

Between the local extreme points, the function is strictly increasing or decreasing.


Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_1.3:1d“