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

Lösung

extrempunkte

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

Maximum (- \frac{2 + 7}{3}, \frac{34 + 14 7}{27} - 2), Minimum (\frac{- 2 + 7}{3}, \frac{34 - 14 7}{27} - 2)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} + 4 x - 1

Intervalle finden:

Ansteigend

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

Absteigend

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

Ansteigend

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

Stecke

x = - \frac{2 + 7}{3}

x^{3} + 2 x^{2} - x - 2 : \frac{34 + 14 7}{27} - 2

Maximum (- \frac{2 + 7}{3}, \frac{34 + 14 7}{27} - 2)

Stecke

x = \frac{- 2 + 7}{3}

x^{3} + 2 x^{2} - x - 2 : \frac{34 - 14 7}{27} - 2

Minimum (\frac{- 2 + 7}{3}, \frac{34 - 14 7}{27} - 2)

Maximum (- \frac{2 + 7}{3}, \frac{34 + 14 7}{27} - 2), Minimum (\frac{- 2 + 7}{3}, \frac{34 - 14 7}{27} - 2)

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

e x t re m e f (x) = 2 x^{2} - 4 x y + 3 y^{2} - 8 x + 8 y - 1 = 0

e x t re m e f (x) = x^{3} + 3 y^{3} + 3 x^{2} + 3 y^{2} + 24

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

e x t re m e f (x) = 9.71 x^{2} + 61.579 x + 943.59