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Beliebt Funktionen >

extreme f(x)=x^3-12x^2+45x+2

Lösung

extrempunkte

f (x) = x^{3} - 12 x^{2} + 45 x + 2

Lösung

Maximum (3, 56), Minimum (5, 52)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 24 x + 45

Intervalle finden:

Ansteigend

: - \infty < x < 3,

Absteigend

: 3 < x < 5,

Ansteigend

: 5 < x < \infty

Stecke

x = 3

in

x^{3} - 12 x^{2} + 45 x + 2 : 56

Maximum (3, 56)

Stecke

x = 5

in

x^{3} - 12 x^{2} + 45 x + 2 : 52

Minimum (5, 52)

Maximum (3, 56), Minimum (5, 52)

Graph

Beliebte Beispiele

extreme f(x)=-5x^3-4x^4

e x t re m e f (x) = - 5 x^{3} - 4 x^{4}

extreme f(x)=x^2+3y^2-2x+18y

e x t re m e f (x) = x^{2} + 3 y^{2} - 2 x + 18 y

extreme f(x)=-x^2-x+1,-1<= x<= 1

e x t re m e f (x) = - x^{2} - x + 1, - 1 \leq x \leq 1

extreme f(x)=e^{0.5x}+256^{-0.5x}

e x t re m e f (x) = e^{0.5 x} + 25 6^{- 0.5 x}

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

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