extreme f(x)= 1/3 x^3-1/3 x^2-2x

Lösung

extrempunkte

f (x) = \frac{1}{3} x^{3} - \frac{1}{3} x^{2} - 2 x

Maximum (\frac{1 - 19}{3}, \frac{38 19 - 56}{81}), Minimum (\frac{1 + 19}{3}, \frac{- 56 - 38 19}{81})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < \frac{- 19 + 1}{3},

Absteigend

: \frac{- 19 + 1}{3} < x < \frac{19 + 1}{3},

Ansteigend

: \frac{19 + 1}{3} < x < \infty

Stecke

x = \frac{1 - 19}{3}

\frac{1}{3} x^{3} - \frac{1}{3} x^{2} - 2 x : \frac{38 19 - 56}{81}

Maximum (\frac{1 - 19}{3}, \frac{38 19 - 56}{81})

Stecke

x = \frac{1 + 19}{3}

\frac{1}{3} x^{3} - \frac{1}{3} x^{2} - 2 x : \frac{- 56 - 38 19}{81}

Minimum (\frac{1 + 19}{3}, \frac{- 56 - 38 19}{81})

Maximum (\frac{1 - 19}{3}, \frac{38 19 - 56}{81}), Minimum (\frac{1 + 19}{3}, \frac{- 56 - 38 19}{81})

e x t re m e F (x, y) = x^{3} ln (y^{2} + 1) - 2 y

e x t re m e f (x) = 1 + 6 x^{2} - x^{3}

e x t re m e 2 x + 10

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

e x t re m e f (x) = 2 x^{4} - 4 x^{2} + 6