extreme f(x)=2x^3+3x^2-2x-2

Lösung

extrempunkte

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

Maximum (- \frac{3 + 21}{6}, \frac{27 + 7 21}{18} - 2), Minimum (\frac{- 3 + 21}{6}, \frac{27 - 7 21}{18} - 2)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{7}{2 3} - \frac{1}{2},

Absteigend

: - \frac{7}{2 3} - \frac{1}{2} < x < \frac{7}{2 3} - \frac{1}{2},

Ansteigend

: \frac{7}{2 3} - \frac{1}{2} < x < \infty

Stecke

x = - \frac{3 + 21}{6}

2 x^{3} + 3 x^{2} - 2 x - 2 : \frac{27 + 7 21}{18} - 2

Maximum (- \frac{3 + 21}{6}, \frac{27 + 7 21}{18} - 2)

Stecke

x = \frac{- 3 + 21}{6}

2 x^{3} + 3 x^{2} - 2 x - 2 : \frac{27 - 7 21}{18} - 2

Minimum (\frac{- 3 + 21}{6}, \frac{27 - 7 21}{18} - 2)

Maximum (- \frac{3 + 21}{6}, \frac{27 + 7 21}{18} - 2), Minimum (\frac{- 3 + 21}{6}, \frac{27 - 7 21}{18} - 2)

e x t re m e f (x, y) = 60 x + 34 y - 4 x y - 6 x^{2} - 3 y^{2} + 5

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

e x t re m e f (x) = x^{3} - 12 x^{2} + 45 x + 2

e x t re m e f (x) = - 5 x^{3} - 4 x^{4}

e x t re m e f (x) = x^{2} + 3 y^{2} - 2 x + 18 y