extreme y=-(x-1)(x+2)^3

Lösung

extrempunkte

y = - (x - 1) (x + 2)^{3}

Sattel (- 2, 0), Maximum (\frac{1}{4}, \frac{2187}{256})

Schritte zur Lösung

f^{'} (x) = - (x + 2)^{3} - 3 x^{3} - 9 x^{2} + 12

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < \frac{1}{4},

Absteigend

: \frac{1}{4} < x < \infty

Stecke

x = - 2

- (x - 1) (x + 2)^{3} : 0

Sattel (- 2, 0)

Stecke

x = \frac{1}{4}

- (x - 1) (x + 2)^{3} : \frac{2187}{256}

Maximum (\frac{1}{4}, \frac{2187}{256})

Sattel (- 2, 0), Maximum (\frac{1}{4}, \frac{2187}{256})

e x t re m e x^{4} - 4 x^{3} + 14

e x t re m e f (x) = \frac{2 x ^{2} + 18}{x}

e x t re m e f (x) = - x^{2} - 15.9 x - 57

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

e x t re m e f (x) = \frac{- x ^{2} - 10 x - 13}{x + 9}