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Antwort 1.3:1
Aus Online Mathematik Brückenkurs 2
| a)
| Stationärer Punkt: | \displaystyle x=0
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| Sattelpunkt: | Keine
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| Lokales Minime: | \displaystyle x=0
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| Lokales Maxima: | Keine
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| Globales Minima: | \displaystyle x=0
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| Globales Maxima: | Keine
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| Streng steigend: | \displaystyle x\ge0
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| Streng fallend: | \displaystyle x\le0
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| b)
| Stationärer Punkt: | \displaystyle x=-1, \displaystyle x=1
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| Sattelpunkt: | Keine
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| Lokales Minime: | \displaystyle x=-3, \displaystyle x=1
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| Lokales Maxima: | \displaystyle x=-1, \displaystyle x=2
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| Globales Minima: | \displaystyle x=-3
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| Globales Maxima: | \displaystyle x=-1
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| Streng steigend: | \displaystyle [-3,-1], \displaystyle [1,2]
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| Streng fallend: | \displaystyle [-1,1]
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| c)
| Critical point:
| \displaystyle x=-2, \displaystyle x=-1, \displaystyle x=\tfrac{1}{2}
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| Sattelpunkt: | \displaystyle x=-1
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| Lokales Minime: | \displaystyle x=-2, \displaystyle x=2
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| Lokales Maxima: | \displaystyle x=-3, \displaystyle x=\tfrac{1}{2}
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| Globales Minima: | \displaystyle x=-2
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| Globales Maxima: | \displaystyle x=-3
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| Streng steigend: | \displaystyle [-2,\tfrac{1}{2}]
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| Streng fallend: | \displaystyle [-3,-2], \displaystyle [\tfrac{1}{2},2]
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| d)
| Stationärer Punkt:
| \displaystyle x=-\tfrac{5}{2}, \displaystyle x=\tfrac{1}{2}
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| Sattelpunkt: | Keine
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| Lokales Minime:
| \displaystyle x=-\tfrac{5}{2}, \displaystyle x=-\tfrac{1}{2}, \displaystyle x=2
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| Lokales Maxima:
| \displaystyle x=-3, \displaystyle x=-1, \displaystyle x=\tfrac{1}{2}
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| Globales Minima: | \displaystyle x=-\tfrac{5}{2}
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| Globales Maxima: | \displaystyle x=-1
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| Streng steigend:
| \displaystyle [-\tfrac{5}{2},-1], \displaystyle [-\tfrac{1}{2},\tfrac{1}{2}]
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| Streng fallend:
| \displaystyle [-3,-\tfrac{5}{2}], \displaystyle [-1,-\tfrac{1}{2}], \displaystyle [\tfrac{1}{2},2]
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