extreme f(x)=-x^2(x-4)(x+4)

Lösung

extrempunkte

f (x) = - x^{2} (x - 4) (x + 4)

Maximum (- 22, 64), Minimum (0, 0), Maximum (22, 64)

Schritte zur Lösung

f^{'} (x) = - 4 x^{3} + 32 x

Intervalle finden:

Ansteigend

: - \infty < x < - 22,

Absteigend

: - 22 < x < 0,

Ansteigend

: 0 < x < 22,

Absteigend

: 22 < x < \infty

Stecke

x = - 22

- x^{2} (x - 4) (x + 4) : 64

Maximum (- 22, 64)

Stecke

x = 0

- x^{2} (x - 4) (x + 4) : 0

Minimum (0, 0)

Stecke

x = 22

- x^{2} (x - 4) (x + 4) : 64

Maximum (22, 64)

Maximum (- 22, 64), Minimum (0, 0), Maximum (22, 64)

e x t re m e e^{9 x} + e^{- x}

e x t re m e f (x) = x^{3} - 3 x y^{2} - 3 y^{2} + 12 y

e x t re m e x^{2} y - 6 y^{2} - 3 x^{2}

e x t re m e f (x) = - x^{2} + 7 x - 7

e x t re m e f (x) = x^{3} + x^{2} - 46 x + 80