extreme f(x)=2(x-1)(x-2)(x+3)

Lösung

extrempunkte

f (x) = 2 (x - 1) (x - 2) (x + 3)

Maximum (- \frac{7}{3}, - \frac{26 7}{3 3} + 12 + 621), Minimum (\frac{7}{3}, \frac{26 7}{3 3} + 12 - 621)

Schritte zur Lösung

f^{'} (x) = 2 (3 x^{2} - 7)

Intervalle finden:

Ansteigend

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

Absteigend

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

Ansteigend

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

Stecke

x = - \frac{7}{3}

2 (x - 1) (x - 2) (x + 3) : - \frac{26 7}{3 3} + 12 + 621

Maximum (- \frac{7}{3}, - \frac{26 7}{3 3} + 12 + 621)

Stecke

x = \frac{7}{3}

2 (x - 1) (x - 2) (x + 3) : \frac{26 7}{3 3} + 12 - 621

Minimum (\frac{7}{3}, \frac{26 7}{3 3} + 12 - 621)

Maximum (- \frac{7}{3}, - \frac{26 7}{3 3} + 12 + 621), Minimum (\frac{7}{3}, \frac{26 7}{3 3} + 12 - 621)

e x t re m e f (x, y) = x^{2} + 16 y^{2}

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

e x t re m e \frac{( π + 4 ) x ^{2} - 640 x + 25600}{π}

e x t re m e f (x) = x (22 - x)

y (C, t) = C_{2} e^{- 6 t}