extreme x^3-2x^2-4x-4

Lösung

extrempunkte

x^{3} - 2 x^{2} - 4 x - 4

Maximum (- \frac{2}{3}, - \frac{68}{27}), Minimum (2, - 12)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 4 x - 4

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{2}{3},

Absteigend

: - \frac{2}{3} < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - \frac{2}{3}

x^{3} - 2 x^{2} - 4 x - 4 : - \frac{68}{27}

Maximum (- \frac{2}{3}, - \frac{68}{27})

Stecke

x = 2

x^{3} - 2 x^{2} - 4 x - 4 : - 12

Minimum (2, - 12)

Maximum (- \frac{2}{3}, - \frac{68}{27}), Minimum (2, - 12)

e x t re m e 9 x^{3} - 7 x^{2} + 3 x + 10

e x t re m e f (x) = 4 + 27 x - x^{3}

e x t re m e f (x) = - \frac{8 x}{( x ^{2} + 1 ) ^{2}}

e x t re m e f (x) = \frac{x}{( 1 + x ) ^{2}}

e x t re m e y = x^{2} - 4 x + 19