extreme f(x)=-2/5 x^5+5x^4-16x^3-19

Lösung

extrempunkte

f (x) = - \frac{2}{5} x^{5} + 5 x^{4} - 16 x^{3} - 19

Sattel (0, - 19), Minimum (4, - \frac{863}{5}), Maximum (6, - \frac{527}{5})

Schritte zur Lösung

f^{'} (x) = - 2 x^{4} + 20 x^{3} - 48 x^{2}

Intervalle finden:

Absteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 4,

Ansteigend

: 4 < x < 6,

Absteigend

: 6 < x < \infty

Stecke

x = 0

- \frac{2}{5} x^{5} + 5 x^{4} - 16 x^{3} - 19 : - 19

Sattel (0, - 19)

Stecke

x = 4

- \frac{2}{5} x^{5} + 5 x^{4} - 16 x^{3} - 19 : - \frac{863}{5}

Minimum (4, - \frac{863}{5})

Stecke

x = 6

- \frac{2}{5} x^{5} + 5 x^{4} - 16 x^{3} - 19 : - \frac{527}{5}

Maximum (6, - \frac{527}{5})

Sattel (0, - 19), Minimum (4, - \frac{863}{5}), Maximum (6, - \frac{527}{5})

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

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

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

e x t re m e f (x) = x^{2} + 3 x + 1

e x t re m e x - 3 x