extreme f(x)=-2x^3+9x^2-10x+3

Lösung

extrempunkte

f (x) = - 2 x^{3} + 9 x^{2} - 10 x + 3

Minimum (\frac{9 - 21}{6}, \frac{- 27 - 7 21}{18} + 3), Maximum (\frac{9 + 21}{6}, \frac{7 21 - 27}{18} + 3)

Schritte zur Lösung

f^{'} (x) = - 6 x^{2} + 18 x - 10

Intervalle finden:

Absteigend

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

Ansteigend

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

Absteigend

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

Stecke

x = \frac{9 - 21}{6}

- 2 x^{3} + 9 x^{2} - 10 x + 3 : \frac{- 27 - 7 21}{18} + 3

Minimum (\frac{9 - 21}{6}, \frac{- 27 - 7 21}{18} + 3)

Stecke

x = \frac{9 + 21}{6}

- 2 x^{3} + 9 x^{2} - 10 x + 3 : \frac{7 21 - 27}{18} + 3

Maximum (\frac{9 + 21}{6}, \frac{7 21 - 27}{18} + 3)

Minimum (\frac{9 - 21}{6}, \frac{- 27 - 7 21}{18} + 3), Maximum (\frac{9 + 21}{6}, \frac{7 21 - 27}{18} + 3)

e x t re m e \frac{x ^{4}}{4} - \frac{x ^{3}}{3} - 2 x^{2} + 4 x + 3

e x t re m e f (x, y) = 4 x y - x^{2} - y^{2} - 14 x + 4 y + 10

e x t re m e y = \frac{sin ( x )}{x} {- 2, π \leq x \leq 2 π}

e x t re m e 2 x^{4} + y^{2} - x^{2} - 2 y

e x t re m e f (x, y) = 1 - \frac{x ^{2}}{4} - y^{2}