extreme 3x(x-3)^3

Lösung

extrempunkte

3 x (x - 3)^{3}

Minimum (\frac{3}{4}, - \frac{6561}{256}), Sattel (3, 0)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < \frac{3}{4},

Ansteigend

: \frac{3}{4} < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = \frac{3}{4}

3 x (x - 3)^{3} : - \frac{6561}{256}

Minimum (\frac{3}{4}, - \frac{6561}{256})

Stecke

x = 3

3 x (x - 3)^{3} : 0

Sattel (3, 0)

Minimum (\frac{3}{4}, - \frac{6561}{256}), Sattel (3, 0)

e x t re m e f (x) = x^{\frac{4}{3}} + 4^{\frac{1}{3}}

e x t re m e f (x, y) = 2 y^{2} - x y + 6 y^{2}

e x t re m e - \frac{1}{80} t^{2} + \frac{9}{40} t - \frac{17}{80}

e x t re m e 3 x^{2} - 4 x - 1

e x t re m e f (x) = f (x) = 3 x \frac{5}{3} - 15 x \frac{2}{3}