extreme f(x)=24x^3-3x^4

Lösung

extrempunkte

f (x) = 24 x^{3} - 3 x^{4}

Sattel (0, 0), Maximum (6, 1296)

Schritte zur Lösung

f^{'} (x) = 72 x^{2} - 12 x^{3}

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 6,

Absteigend

: 6 < x < \infty

Stecke

x = 0

24 x^{3} - 3 x^{4} : 0

Sattel (0, 0)

Stecke

x = 6

24 x^{3} - 3 x^{4} : 1296

Maximum (6, 1296)

Sattel (0, 0), Maximum (6, 1296)

e x t re m e 3 x^{2} - 12 x y + y^{3} + 3 y^{2}

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

e x t re m e 1 + \frac{7}{x} - \frac{3}{x ^{2}}

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

e x t re m e f (x) = 5 + 54 x + 2 x^{3}, 0 \leq x \leq 4