extreme 1/3 x^3+1/2 x^2-2x

Lösung

extrempunkte

\frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 2 x

Maximum (- 2, \frac{10}{3}), Minimum (1, - \frac{7}{6})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 2

\frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 2 x : \frac{10}{3}

Maximum (- 2, \frac{10}{3})

Stecke

x = 1

\frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 2 x : - \frac{7}{6}

Minimum (1, - \frac{7}{6})

Maximum (- 2, \frac{10}{3}), Minimum (1, - \frac{7}{6})

e x t re m e f (x) = 12 x - x^{3} - y (y^{2} + 3 y - 9) + 4

e x t re m e f (x) = 64 - x^{2}

e x t re m e f (x, y) = x y - 4 y - 16 x + 64

e x t re m e y = cos (x)

e x t re m e 2 x^{2} + 24 x - 6