Antwort 1.3:1

Aus Online Mathematik Brückenkurs 2

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K (Answer 1.3:1 moved to Antwort 1.3:1: Robot: moved page)
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||a)
||a)
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||Critical&nbsp;point:||<math>x=0</math>
+
||Stationärer&nbsp;Punkt:||<math>x=0</math>
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|-
||
||
-
||Inflexion&nbsp;point:||None
+
||Sattelpunkt:||Keine
|-
|-
||
||
-
||Local&nbsp;min:||<math>x=0</math>
+
||Lokales&nbsp;Minime:||<math>x=0</math>
|-
|-
||
||
-
||Local&nbsp;max:||None
+
||Lokales&nbsp;Maxima:||Keine
|-
|-
||
||
-
||Global&nbsp;min:||<math>x=0</math>
+
||Globales&nbsp;Minima:||<math>x=0</math>
|-
|-
||
||
-
||Global&nbsp;max:||None
+
||Globales&nbsp;Maxima:||Keine
|-
|-
||
||
-
||Strictly&nbsp;incr.:||<math>x\ge0</math>
+
||Streng&nbsp;steigend:||<math>x\ge0</math>
|-
|-
||
||
-
||Strictly&nbsp;decr.:||<math>x\le0</math>
+
||Streng&nbsp;fallend:||<math>x\le0</math>
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|}
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{| cellspacing="10px"
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||b)
||b)
-
||Critical&nbsp;point:||<math>x=-1</math>, <math>x=1</math>
+
||Stationärer&nbsp;Punkt:||<math>x=-1</math>, <math>x=1</math>
|-
|-
||
||
-
||Inflexion&nbsp;point:||None
+
||Sattelpunkt:||Keine
|-
|-
||
||
-
||Local&nbsp;min:||<math>x=-3</math>, <math>x=1</math>
+
||Lokales&nbsp;Minime:||<math>x=-3</math>, <math>x=1</math>
|-
|-
||
||
-
||Local&nbsp;max:||<math>x=-1</math>, <math>x=2</math>
+
||Lokales&nbsp;Maxima:||<math>x=-1</math>, <math>x=2</math>
|-
|-
||
||
-
||Global&nbsp;min:||<math>x=-3</math>
+
||Globales&nbsp;Minima:||<math>x=-3</math>
|-
|-
||
||
-
||Global&nbsp;max:||<math>x=-1</math>
+
||Globales&nbsp;Maxima:||<math>x=-1</math>
|-
|-
||
||
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||Strictly&nbsp;incr.:||<math>[-3,-1]</math>, <math>[1,2]</math>
+
||Streng&nbsp;steigend:||<math>[-3,-1]</math>, <math>[1,2]</math>
|-
|-
||
||
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||Strictly&nbsp;decr.:||<math>[-1,1]</math>
+
||Streng&nbsp;fallend:||<math>[-1,1]</math>
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|-
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Zeile 60: Zeile 60:
|-
|-
||
||
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||Inflexion&nbsp;point:||<math>x=-1</math>
+
||Sattelpunkt:||<math>x=-1</math>
|-
|-
||
||
-
||Local&nbsp;min:||<math>x=-2</math>, <math>x=2</math>
+
||Lokales&nbsp;Minime:||<math>x=-2</math>, <math>x=2</math>
|-
|-
||
||
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||Local&nbsp;max:||<math>x=-3</math>, <math>x=\tfrac{1}{2}</math>
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||Lokales&nbsp;Maxima:||<math>x=-3</math>, <math>x=\tfrac{1}{2}</math>
|-
|-
||
||
-
||Global&nbsp;min:||<math>x=-2</math>
+
||Globales&nbsp;Minima:||<math>x=-2</math>
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|-
||
||
-
||Global&nbsp;max:||<math>x=-3</math>
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||Globales&nbsp;Maxima:||<math>x=-3</math>
|-
|-
||
||
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||Strictly&nbsp;incr.:||<math>[-2,\tfrac{1}{2}]</math>
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||Streng&nbsp;steigend:||<math>[-2,\tfrac{1}{2}]</math>
|-
|-
||
||
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||Strictly&nbsp;decr.:||<math>[-3,-2]</math>, <math>[\tfrac{1}{2},2]</math>
+
||Streng&nbsp;fallend:||<math>[-3,-2]</math>, <math>[\tfrac{1}{2},2]</math>
|}
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| width="50%" valign="top" |
{| cellspacing="10px"
{| cellspacing="10px"
| valign="top" |d)
| valign="top" |d)
-
| valign="top" |Critical&nbsp;point:
+
| valign="top" |Stationärer&nbsp;Punkt:
| valign="top" |<math>x=-\tfrac{5}{2}</math>, <math>x=\tfrac{1}{2}</math>
| valign="top" |<math>x=-\tfrac{5}{2}</math>, <math>x=\tfrac{1}{2}</math>
|-
|-
||
||
-
||Inflexion&nbsp;point:||None
+
||Sattelpunkt:||Keine
|-
|-
||
||
-
| valign="top" |Local&nbsp;min:
+
| valign="top" |Lokales&nbsp;Minime:
| 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>
|-
|-
||
||
-
| valign="top" |Local&nbsp;max:
+
| valign="top" |Lokales&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>
|-
|-
||
||
-
||Global&nbsp;min:||<math>x=-\tfrac{5}{2}</math>
+
||Globales&nbsp;Minima:||<math>x=-\tfrac{5}{2}</math>
|-
|-
||
||
-
||Global&nbsp;max:||<math>x=-1</math>
+
||Globales&nbsp;Maxima:||<math>x=-1</math>
|-
|-
||
||
-
| valign="top" |Strictly&nbsp;incr.:
+
| valign="top" |Streng&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>
|-
|-
||
||
-
| valign="top" |Strictly&nbsp;decr.:
+
| valign="top" |Streng&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 14:35, 26. Apr. 2009

a) Stationärer Punkt:\displaystyle x=0
Sattelpunkt:Keine
Lokales Minime:\displaystyle x=0
Lokales Maxima:Keine
Globales Minima:\displaystyle x=0
Globales Maxima:Keine
Streng steigend:\displaystyle x\ge0
Streng fallend:\displaystyle x\le0
b) Stationärer Punkt:\displaystyle x=-1, \displaystyle x=1
Sattelpunkt:Keine
Lokales Minime:\displaystyle x=-3, \displaystyle x=1
Lokales Maxima:\displaystyle x=-1, \displaystyle x=2
Globales Minima:\displaystyle x=-3
Globales Maxima:\displaystyle x=-1
Streng steigend:\displaystyle [-3,-1], \displaystyle [1,2]
Streng fallend:\displaystyle [-1,1]
c) Critical point: \displaystyle x=-2, \displaystyle x=-1, \displaystyle x=\tfrac{1}{2}
Sattelpunkt:\displaystyle x=-1
Lokales Minime:\displaystyle x=-2, \displaystyle x=2
Lokales Maxima:\displaystyle x=-3, \displaystyle x=\tfrac{1}{2}
Globales Minima:\displaystyle x=-2
Globales Maxima:\displaystyle x=-3
Streng steigend:\displaystyle [-2,\tfrac{1}{2}]
Streng fallend:\displaystyle [-3,-2], \displaystyle [\tfrac{1}{2},2]
d) Stationärer Punkt: \displaystyle x=-\tfrac{5}{2}, \displaystyle x=\tfrac{1}{2}
Sattelpunkt:Keine
Lokales Minime: \displaystyle x=-\tfrac{5}{2}, \displaystyle x=-\tfrac{1}{2}, \displaystyle x=2
Lokales Maxima: \displaystyle x=-3, \displaystyle x=-1, \displaystyle x=\tfrac{1}{2}
Globales Minima:\displaystyle x=-\tfrac{5}{2}
Globales Maxima:\displaystyle x=-1
Streng steigend: \displaystyle [-\tfrac{5}{2},-1], \displaystyle [-\tfrac{1}{2},\tfrac{1}{2}]
Streng fallend: \displaystyle [-3,-\tfrac{5}{2}], \displaystyle [-1,-\tfrac{1}{2}], \displaystyle [\tfrac{1}{2},2]
Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/Antwort_1.3:1“