extreme f(x)=-462x+64x^2-2x^3

Lösung

extrempunkte

f (x) = - 462 x + 64 x^{2} - 2 x^{3}

Minimum (\frac{32 - 331}{3}, - 154 (32 - 331) + \frac{131072 - 5482 331}{27}), Maximum (\frac{32 + 331}{3}, - 154 (32 + 331) + \frac{131072 + 5482 331}{27})

Schritte zur Lösung

f^{'} (x) = - 462 + 128 x - 6 x^{2}

Intervalle finden:

Absteigend

: - \infty < x < \frac{- 331 + 32}{3},

Ansteigend

: \frac{- 331 + 32}{3} < x < \frac{331 + 32}{3},

Absteigend

: \frac{331 + 32}{3} < x < \infty

Stecke

x = \frac{32 - 331}{3}

- 462 x + 64 x^{2} - 2 x^{3} : - 154 (32 - 331) + \frac{131072 - 5482 331}{27}

Minimum (\frac{32 - 331}{3}, - 154 (32 - 331) + \frac{131072 - 5482 331}{27})

Stecke

x = \frac{32 + 331}{3}

- 462 x + 64 x^{2} - 2 x^{3} : - 154 (32 + 331) + \frac{131072 + 5482 331}{27}

Maximum (\frac{32 + 331}{3}, - 154 (32 + 331) + \frac{131072 + 5482 331}{27})

Minimum (\frac{32 - 331}{3}, - 154 (32 - 331) + \frac{131072 - 5482 331}{27}), Maximum (\frac{32 + 331}{3}, - 154 (32 + 331) + \frac{131072 + 5482 331}{27})

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

e x t re m e f (x) = - 5 x^{7} ln (2 x), (0, 6)

e x t re m e - x^{3} + 12 x

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

e x t re m e y = x^{2} - 12 x + 1