extreme y=x^3-8x^2-12x+8

Lösung

extrempunkte

y = x^{3} - 8 x^{2} - 12 x + 8

Maximum (- \frac{2}{3}, \frac{328}{27}), Minimum (6, - 136)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 16 x - 12

Intervalle finden:

Ansteigend

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

Absteigend

: - \frac{2}{3} < x < 6,

Ansteigend

: 6 < x < \infty

Stecke

x = - \frac{2}{3}

x^{3} - 8 x^{2} - 12 x + 8 : \frac{328}{27}

Maximum (- \frac{2}{3}, \frac{328}{27})

Stecke

x = 6

x^{3} - 8 x^{2} - 12 x + 8 : - 136

Minimum (6, - 136)

Maximum (- \frac{2}{3}, \frac{328}{27}), Minimum (6, - 136)

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

e x t re m e e^{7 x} + e^{- x}

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

e x t re m e f (x) = x 81 - x^{2}

e x t re m e S (a, d) = a + (n - 1) d