extreme f(x)=-(x-1)^2(x-5)

Lösung

extrempunkte

f (x) = - (x - 1)^{2} (x - 5)

Minimum (1, 0), Maximum (\frac{11}{3}, \frac{256}{27})

Schritte zur Lösung

f^{'} (x) = - 3 x^{2} + 14 x - 11

Intervalle finden:

Absteigend

: - \infty < x < 1,

Ansteigend

: 1 < x < \frac{11}{3},

Absteigend

: \frac{11}{3} < x < \infty

Stecke

x = 1

- (x - 1)^{2} (x - 5) : 0

Minimum (1, 0)

Stecke

x = \frac{11}{3}

- (x - 1)^{2} (x - 5) : \frac{256}{27}

Maximum (\frac{11}{3}, \frac{256}{27})

Minimum (1, 0), Maximum (\frac{11}{3}, \frac{256}{27})

e x t re m e f (x, y) = 3 x^{3} - 9 x + 9 x y^{2}

e x t re m e ln (x + 2) (x - 1)^{2}

e x t re m e f (x, y) = 4 x + 6 y - x^{2} - y^{2} + 9

e x t re m e y = \frac{x}{x ^{2} + 9}

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