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