extreme f(x)=-3x^4-7x^3+23

Lösung

extrempunkte

f (x) = - 3 x^{4} - 7 x^{3} + 23

Maximum (- \frac{7}{4}, \frac{8289}{256}), Sattel (0, 23)

Schritte zur Lösung

f^{'} (x) = - 12 x^{3} - 21 x^{2}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{7}{4},

Absteigend

: - \frac{7}{4} < x < 0,

Absteigend

: 0 < x < \infty

Stecke

x = - \frac{7}{4}

- 3 x^{4} - 7 x^{3} + 23 : \frac{8289}{256}

Maximum (- \frac{7}{4}, \frac{8289}{256})

Stecke

x = 0

- 3 x^{4} - 7 x^{3} + 23 : 23

Sattel (0, 23)

Maximum (- \frac{7}{4}, \frac{8289}{256}), Sattel (0, 23)

e x t re m e f (x) = x 6 - x

e x t re m e f (x) = 8 x^{3} + 81 x^{2} - 42 x - 8

e x t re m e f (x, y) = x^{3} + 3 x y^{2} - 15 x + y^{3} - 15 y

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

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