extreme f(x)=-x^4-4x^3+7

Lösung

extrempunkte

f (x) = - x^{4} - 4 x^{3} + 7

Maximum (- 3, 34), Sattel (0, 7)

Schritte zur Lösung

f^{'} (x) = - 4 x^{3} - 12 x^{2}

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < 0,

Absteigend

: 0 < x < \infty

Stecke

x = - 3

- x^{4} - 4 x^{3} + 7 : 34

Maximum (- 3, 34)

Stecke

x = 0

- x^{4} - 4 x^{3} + 7 : 7

Sattel (0, 7)

Maximum (- 3, 34), Sattel (0, 7)

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

e x t re m e f (x, y) = 3 x + 5 y - 2 x^{2} - 3 y^{2}

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

e x t re m e f (x) = 2 x + \frac{1}{x}

e x t re m e f (x) = e^{x^{2} - 3 x - 1}, - 3 \leq x \leq 3