extreme f(x)=-x^3+15x^2+13

Lösung

extrempunkte

f (x) = - x^{3} + 15 x^{2} + 13

Minimum (0, 13), Maximum (10, 513)

Schritte zur Lösung

f^{'} (x) = - 3 x^{2} + 30 x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 10,

Absteigend

: 10 < x < \infty

Stecke

x = 0

- x^{3} + 15 x^{2} + 13 : 13

Minimum (0, 13)

Stecke

x = 10

- x^{3} + 15 x^{2} + 13 : 513

Maximum (10, 513)

Minimum (0, 13), Maximum (10, 513)

e x t re m e x^{\frac{1}{3}} (x^{2} - 9), - 4 \leq x \leq 2

e x t re m e f (x) = x e^{- x^{2}} [0.2]

e x t re m e f (x) = - 2 x^{3} + 30 x^{2} - 54 x + 6

e x t re m e f (x) = - 2 x^{3} + 30 x^{2} - 54 x + 8

e x t re m e - 6 x + x^{2}