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Beliebt Funktionen >

extreme f(x)=e^{x^3-6x^2}

Lösung

extrempunkte

f (x) = e^{x^{3} - 6 x^{2}}

Lösung

Maximum (0, 1), Minimum (4, \frac{1}{e ^{32}})

Schritte zur Lösung

f^{'} (x) = e^{x^{3} - 6 x^{2}} (3 x^{2} - 12 x)

Intervalle finden:

Absteigend

: 0 < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = 0

in

e^{x^{3} - 6 x^{2}} : 1

Maximum (0, 1)

Stecke

x = 4

in

e^{x^{3} - 6 x^{2}} : \frac{1}{e ^{32}}

Minimum (4, \frac{1}{e ^{32}})

Maximum (0, 1), Minimum (4, \frac{1}{e ^{32}})

Graph

Beliebte Beispiele

extreme p(a,c)=a+2+c

e x t re m e p (a, c) = a + 2 + c

extreme f(x)=40e^{2x}-5e^x

e x t re m e f (x) = 40 e^{2 x} - 5 e^{x}

extreme f(x)=x+(49)/x ,2<= x<= 12

e x t re m e f (x) = x + \frac{49}{x}, 2 \leq x \leq 12

extreme f(x)=3-6x^2

e x t re m e f (x) = 3 - 6 x^{2}

extreme f(x,y)=x^2+xy-y^2-y

e x t re m e f (x, y) = x^{2} + x y - y^{2} - y