extreme f(x)=x(23-41+2x)(41/2-x)

Lösung

extrempunkte

f (x) = x (23 - 41 + 2 x) (\frac{41}{2} - x)

Minimum (\frac{59 - 1267}{6}, \frac{9440 - 1267 1267}{54}), Maximum (\frac{59 + 1267}{6}, \frac{1267 1267 + 9440}{54})

Schritte zur Lösung

f^{'} (x) = - 6 x^{2} + 118 x - 369

Intervalle finden:

Absteigend

: - \infty < x < \frac{- 1267 + 59}{6},

Ansteigend

: \frac{- 1267 + 59}{6} < x < \frac{1267 + 59}{6},

Absteigend

: \frac{1267 + 59}{6} < x < \infty

Stecke

x = \frac{59 - 1267}{6}

x (23 - 41 + 2 x) (\frac{41}{2} - x) : \frac{9440 - 1267 1267}{54}

Minimum (\frac{59 - 1267}{6}, \frac{9440 - 1267 1267}{54})

Stecke

x = \frac{59 + 1267}{6}

x (23 - 41 + 2 x) (\frac{41}{2} - x) : \frac{1267 1267 + 9440}{54}

Maximum (\frac{59 + 1267}{6}, \frac{1267 1267 + 9440}{54})

Minimum (\frac{59 - 1267}{6}, \frac{9440 - 1267 1267}{54}), Maximum (\frac{59 + 1267}{6}, \frac{1267 1267 + 9440}{54})

e x t re m e x^{3} - 3 x^{2} - 9 x + 2

e x t re m e x^{3} - 3 x^{2} - 9 x + 4

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

e x t re m e f (x) = x 5 - x^{2}

e x t re m e P (x, y) = x^{2} - y^{2} + 6 y - 9