extreme f(x)=(x+1)^2(x-1/2)(x-2)

Lösung

extrempunkte

f (x) = (x + 1)^{2} (x - \frac{1}{2}) (x - 2)

Minimum (- 1, 0), Maximum (\frac{11 - 3 17}{16}, \frac{4131 17 - 16859}{8192} + 1), Minimum (\frac{11 + 3 17}{16}, \frac{- 16859 - 4131 17}{8192} + 1)

Schritte zur Lösung

f^{'} (x) = \frac{1}{2} (x + 1) (8 x^{2} - 11 x - 1)

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < \frac{11 - 3 17}{16},

Absteigend

: \frac{11 - 3 17}{16} < x < \frac{11 + 3 17}{16},

Ansteigend

: \frac{11 + 3 17}{16} < x < \infty

Stecke

x = - 1

(x + 1)^{2} (x - \frac{1}{2}) (x - 2) : 0

Minimum (- 1, 0)

Stecke

x = \frac{11 - 3 17}{16}

(x + 1)^{2} (x - \frac{1}{2}) (x - 2) : \frac{4131 17 - 16859}{8192} + 1

Maximum (\frac{11 - 3 17}{16}, \frac{4131 17 - 16859}{8192} + 1)

Stecke

x = \frac{11 + 3 17}{16}

(x + 1)^{2} (x - \frac{1}{2}) (x - 2) : \frac{- 16859 - 4131 17}{8192} + 1

Minimum (\frac{11 + 3 17}{16}, \frac{- 16859 - 4131 17}{8192} + 1)

Minimum (- 1, 0), Maximum (\frac{11 - 3 17}{16}, \frac{4131 17 - 16859}{8192} + 1), Minimum (\frac{11 + 3 17}{16}, \frac{- 16859 - 4131 17}{8192} + 1)

e x t re m e P (x, y) = x y

e x t re m e x - 2 sin (x) (0.2 π)

e x t re m e f (x, y) = (x + y)^{- 1}

e x t re m e f (x) = x^{2} - 18 x

e x t re m e f (x, y) = 400 - 49 x^{2} - 16 y^{2}