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Antwort 1.3:1
Aus Online Mathematik Brückenkurs 2
a)
Critical point: x = 0
Inflexion point: None
Local min: x = 0
Local max: None
Global min: x = 0
Global max: None
Strictly incr.: x 0
Strictly decr.: x 0
b)
Critical point: x = − 1 x = 1
Inflexion point: None
Local min: x = − 3 x = 1
Local max: x = − 1 x = 2
Global min: x = − 3
Global max: x = − 1
Strictly incr.: [ − 3 − 1] [1 2 ]
Strictly decr.: [ − 1 1 ]
c)
Critical point:
x = − 2 x = − 1 x = 2 1
Inflexion point: x = − 1
Local min: x = − 2 x = 2
Local max: x = − 3 x = 2 1
Global min: x = − 2
Global max: x = − 3
Strictly incr.: [ − 2 2 1 ]
Strictly decr.: [ − 3 − 2] [ 2 1 2 ]
d)
Critical point:
x = − 2 5 x = 2 1
Inflexion point: None
Local min:
x = − 2 5 \displaystyle x=-\tfrac{1}{2} , \displaystyle x=2
Local max:
\displaystyle x=-3 , \displaystyle x=-1 , \displaystyle x=\tfrac{1}{2}
Global min: \displaystyle x=-\tfrac{5}{2}
Global max: \displaystyle x=-1
Strictly incr.:
\displaystyle [-\tfrac{5}{2},-1] , \displaystyle [-\tfrac{1}{2},\tfrac{1}{2}]
Strictly decr.:
\displaystyle [-3,-\tfrac{5}{2}] , \displaystyle [-1,-\tfrac{1}{2}] , \displaystyle [\tfrac{1}{2},2]
