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Antwort 1.3:1

Aus Online Mathematik Brückenkurs 2

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
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||Sattelpunkt:||Keine
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||Sattelpunkte:||Keine
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||Lokales&nbsp;Minime:||<math>x=0</math>
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||Lokales&nbsp;Minimum:||<math>x=0</math>
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||Lokales&nbsp;Maxima:||Keine
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||Lokale&nbsp;Maxima:||Keine
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||Globales&nbsp;Minima:||<math>x=0</math>
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||Globales&nbsp;Minimum:||<math>x=0</math>
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||Globales&nbsp;Maxima:||Keine
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||Globale&nbsp;Maxima:||Keine
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||Streng&nbsp;steigend:||<math>x\ge0</math>
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||Streng&nbsp;monoton&nbsp;steigend:||<math>x\ge0</math>
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||Streng&nbsp;fallend:||<math>x\le0</math>
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||Streng&nbsp;monoton&nbsp;fallend:||<math>x\le0</math>
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Zeile 32: Zeile 32:
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||Sattelpunkt:||Keine
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||Sattelpunkte:||Keine
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||Lokales&nbsp;Minime:||<math>x=-3</math>, <math>x=1</math>
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||Lokale&nbsp;Minima:||<math>x=-3</math>, <math>x=1</math>
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||Lokales&nbsp;Maxima:||<math>x=-1</math>, <math>x=2</math>
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||Lokale&nbsp;Maxima:||<math>x=-1</math>, <math>x=2</math>
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||Globales&nbsp;Minima:||<math>x=-3</math>
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||Globales&nbsp;Minimum:||<math>x=-3</math>
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||Globales&nbsp;Maxima:||<math>x=-1</math>
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||Globales&nbsp;Maximum:||<math>x=-1</math>
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||Streng&nbsp;steigend:||<math>[-3,-1]</math>, <math>[1,2]</math>
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||Streng&nbsp;monoton&nbsp;steigend:||<math>[-3,-1]</math>, <math>[1,2]</math>
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||Streng&nbsp;fallend:||<math>[-1,1]</math>
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||Streng&nbsp;monoton&nbsp;fallend:||<math>[-1,1]</math>
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Zeile 63: Zeile 63:
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||Lokales&nbsp;Minime:||<math>x=-2</math>, <math>x=2</math>
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||Lokale&nbsp;Minima:||<math>x=-2</math>, <math>x=2</math>
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||Lokales&nbsp;Maxima:||<math>x=-3</math>, <math>x=\tfrac{1}{2}</math>
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||Lokale&nbsp;Maxima:||<math>x=-3</math>, <math>x=\tfrac{1}{2}</math>
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||Globales&nbsp;Minima:||<math>x=-2</math>
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||Globales&nbsp;Minimum:||<math>x=-2</math>
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||Globales&nbsp;Maxima:||<math>x=-3</math>
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||Globales&nbsp;Maximum:||<math>x=-3</math>
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||Streng&nbsp;steigend:||<math>[-2,\tfrac{1}{2}]</math>
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||Streng&nbsp;monoton&nbsp;steigend:||<math>[-2,\tfrac{1}{2}]</math>
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||Streng&nbsp;fallend:||<math>[-3,-2]</math>, <math>[\tfrac{1}{2},2]</math>
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||Streng&nbsp;monoton&nbsp;fallend:||<math>[-3,-2]</math>, <math>[\tfrac{1}{2},2]</math>
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| valign="top" |Lokales&nbsp;Minime:
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| valign="top" |Lokale&nbsp;Minima:
| valign="top" |<math>x=-\tfrac{5}{2}</math>, <math>x=-\tfrac{1}{2}</math>, <math>x=2</math>
| valign="top" |<math>x=-\tfrac{5}{2}</math>, <math>x=-\tfrac{1}{2}</math>, <math>x=2</math>
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| valign="top" |Lokales&nbsp;Maxima:
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| valign="top" |Lokale&nbsp;Maxima:
| valign="top" |<math>x=-3</math>, <math>x=-1</math>, <math>x=\tfrac{1}{2}</math>
| valign="top" |<math>x=-3</math>, <math>x=-1</math>, <math>x=\tfrac{1}{2}</math>
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||Globales&nbsp;Minima:||<math>x=-\tfrac{5}{2}</math>
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||Globales&nbsp;Minimum:||<math>x=-\tfrac{5}{2}</math>
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||Globales&nbsp;Maxima:||<math>x=-1</math>
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||Globales&nbsp;Maximum:||<math>x=-1</math>
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| valign="top" |Streng&nbsp;steigend:
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| valign="top" |Streng&nbsp;monoton&nbsp;steigend:
| valign="top" |<math>[-\tfrac{5}{2},-1]</math>, <math>[-\tfrac{1}{2},\tfrac{1}{2}]</math>
| valign="top" |<math>[-\tfrac{5}{2},-1]</math>, <math>[-\tfrac{1}{2},\tfrac{1}{2}]</math>
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| valign="top" |Streng&nbsp;fallend:
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| valign="top" |Streng&nbsp;monoton&nbsp;fallend:
| valign="top" |<math>[-3,-\tfrac{5}{2}]</math>, <math>[-1,-\tfrac{1}{2}]</math>, <math>[\tfrac{1}{2},2]</math>
| valign="top" |<math>[-3,-\tfrac{5}{2}]</math>, <math>[-1,-\tfrac{1}{2}]</math>, <math>[\tfrac{1}{2},2]</math>
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Version vom 13:28, 4. Aug. 2009

a) Stationärer Punkt:x=0
Sattelpunkte:Keine
Lokales Minimum:x=0
Lokale Maxima:Keine
Globales Minimum:x=0
Globale Maxima:Keine
Streng monoton steigend:x0
Streng monoton fallend:x0
b) Stationärer Punkt:x=−1, x=1
Sattelpunkte:Keine
Lokale Minima:x=−3, x=1
Lokale Maxima:x=−1, x=2
Globales Minimum:x=−3
Globales Maximum:x=−1
Streng monoton steigend:[−3−1], [12]
Streng monoton fallend:[−11]
c) Critical point: x=−2, x=−1, x=21
Sattelpunkt:x=−1
Lokale Minima:x=−2, x=2
Lokale Maxima:x=−3, x=21
Globales Minimum:x=−2
Globales Maximum:x=−3
Streng monoton steigend:[−221]
Streng monoton fallend:[−3−2], [212]
d) Stationärer Punkt: x=−25, x=21
Sattelpunkt:Keine
Lokale Minima: x=−25, \displaystyle x=-\tfrac{1}{2}, \displaystyle x=2
Lokale Maxima: \displaystyle x=-3, \displaystyle x=-1, \displaystyle x=\tfrac{1}{2}
Globales Minimum:\displaystyle x=-\tfrac{5}{2}
Globales Maximum:\displaystyle x=-1
Streng monoton steigend: \displaystyle [-\tfrac{5}{2},-1], \displaystyle [-\tfrac{1}{2},\tfrac{1}{2}]
Streng monoton fallend: \displaystyle [-3,-\tfrac{5}{2}], \displaystyle [-1,-\tfrac{1}{2}], \displaystyle [\tfrac{1}{2},2]
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/Antwort_1.3:1“