extreme f(x)=x^4+2x^3-3x^2-4x+4

Lösung

extrempunkte

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

Minimum (- 2, 0), Maximum (- \frac{1}{2}, \frac{81}{16}), Minimum (1, 0)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} + 6 x^{2} - 6 x - 4

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < - \frac{1}{2},

Absteigend

: - \frac{1}{2} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 2

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

Minimum (- 2, 0)

Stecke

x = - \frac{1}{2}

x^{4} + 2 x^{3} - 3 x^{2} - 4 x + 4 : \frac{81}{16}

Maximum (- \frac{1}{2}, \frac{81}{16})

Stecke

x = 1

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

Minimum (1, 0)

Minimum (- 2, 0), Maximum (- \frac{1}{2}, \frac{81}{16}), Minimum (1, 0)

e x t re m e f (x) = x^{2} - 4 x - 1

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

e x t re m e f (x) = 3 x^{5} - 5 x^{3} + 15

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

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