extreme-x^4+4x^3+8x^2

Lösung

extrempunkte

- x^{4} + 4 x^{3} + 8 x^{2}

Maximum (- 1, 3), Minimum (0, 0), Maximum (4, 128)

Schritte zur Lösung

f^{'} (x) = - 4 x^{3} + 12 x^{2} + 16 x

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < 0,

Ansteigend

: 0 < x < 4,

Absteigend

: 4 < x < \infty

Stecke

x = - 1

- x^{4} + 4 x^{3} + 8 x^{2} : 3

Maximum (- 1, 3)

Stecke

x = 0

- x^{4} + 4 x^{3} + 8 x^{2} : 0

Minimum (0, 0)

Stecke

x = 4

- x^{4} + 4 x^{3} + 8 x^{2} : 128

Maximum (4, 128)

Maximum (- 1, 3), Minimum (0, 0), Maximum (4, 128)

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

e x t re m e f (x) = x^{\frac{7}{5}} - 12 x^{\frac{1}{5}}

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

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

e x t re m e x^{4} + 8 x^{3}