extreme f(x)=x^3-3/2 x^2-6x

Lösung

extrempunkte

f (x) = x^{3} - \frac{3}{2} x^{2} - 6 x

Maximum (- 1, \frac{7}{2}), Minimum (2, - 10)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 3 x - 6

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 1

x^{3} - \frac{3}{2} x^{2} - 6 x : \frac{7}{2}

Maximum (- 1, \frac{7}{2})

Stecke

x = 2

x^{3} - \frac{3}{2} x^{2} - 6 x : - 10

Minimum (2, - 10)

Maximum (- 1, \frac{7}{2}), Minimum (2, - 10)

e x t re m e f (x) = \frac{x ^{3}}{( x - 1 ) ^{2}}

e x t re m e f (x, y) = - 6 x^{2} + 5 x y - y^{2} + x + y

e x t re m e f (x) = x^{\frac{5}{3}} - 12 x^{\frac{2}{3}}

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

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