extreme f(x)=-x^3+3x^2+45x-7

Lösung

extrempunkte

f (x) = - x^{3} + 3 x^{2} + 45 x - 7

Minimum (- 3, - 88), Maximum (5, 168)

Schritte zur Lösung

f^{'} (x) = - 3 x^{2} + 6 x + 45

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 5,

Absteigend

: 5 < x < \infty

Stecke

x = - 3

- x^{3} + 3 x^{2} + 45 x - 7 : - 88

Minimum (- 3, - 88)

Stecke

x = 5

- x^{3} + 3 x^{2} + 45 x - 7 : 168

Maximum (5, 168)

Minimum (- 3, - 88), Maximum (5, 168)

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

e x t re m e f (x, y) = \frac{x ^{2} - 2 x y + y}{3 x - 2 y - 6}

e x t re m e f (x) = x^{4} + 6 x^{3} + 12 x^{2} + 8 x + 10

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

e x t re m e 3 x^{4} - x^{6}