extreme f(x)=-6x^3+18x^2+54x-72

Lösung

extrempunkte

f (x) = - 6 x^{3} + 18 x^{2} + 54 x - 72

Minimum (- 1, - 102), Maximum (3, 90)

Schritte zur Lösung

f^{'} (x) = - 18 x^{2} + 36 x + 54

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 3,

Absteigend

: 3 < x < \infty

Stecke

x = - 1

- 6 x^{3} + 18 x^{2} + 54 x - 72 : - 102

Minimum (- 1, - 102)

Stecke

x = 3

- 6 x^{3} + 18 x^{2} + 54 x - 72 : 90

Maximum (3, 90)

Minimum (- 1, - 102), Maximum (3, 90)

e x t re m e f (x) = I n (x + 1 + x^{2})

e x t re m e f (x, y) = 2 x^{4} - x^{2} + 3 y^{2}

e x t re m e f (x) = 2 x^{2} + 4 x - 2

e x t re m e f (x, y) = - 4 x^{2} + 8 x - 9 y^{2} - 18 y - 12

e x t re m e f (x) = 80 x^{2} - \frac{52}{3} x^{3} + x^{4}