extreme y=-5x^3+4x^2+5x-1

Lösung

extrempunkte

y = - 5 x^{3} + 4 x^{2} + 5 x - 1

Minimum (- \frac{- 4 + 91}{15}, \frac{1028 - 182 91}{675} - 1), Maximum (\frac{4 + 91}{15}, \frac{1028 + 182 91}{675} - 1)

Schritte zur Lösung

f^{'} (x) = - 15 x^{2} + 8 x + 5

Intervalle finden:

Absteigend

: - \infty < x < \frac{- 91 + 4}{15},

Ansteigend

: \frac{- 91 + 4}{15} < x < \frac{91 + 4}{15},

Absteigend

: \frac{91 + 4}{15} < x < \infty

Stecke

x = - \frac{- 4 + 91}{15}

- 5 x^{3} + 4 x^{2} + 5 x - 1 : \frac{1028 - 182 91}{675} - 1

Minimum (- \frac{- 4 + 91}{15}, \frac{1028 - 182 91}{675} - 1)

Stecke

x = \frac{4 + 91}{15}

- 5 x^{3} + 4 x^{2} + 5 x - 1 : \frac{1028 + 182 91}{675} - 1

Maximum (\frac{4 + 91}{15}, \frac{1028 + 182 91}{675} - 1)

Minimum (- \frac{- 4 + 91}{15}, \frac{1028 - 182 91}{675} - 1), Maximum (\frac{4 + 91}{15}, \frac{1028 + 182 91}{675} - 1)

e x t re m e f (x) = \frac{9 x ^{2} - 1}{x}

e x t re m e y = 5 + 12 x^{2} - 8 x^{3}

e x t re m e (x + 2) (x + 1) (x - 1) (x - 3)

e x t re m e f (x) = \cdot 0.002 d^{2} + 0.7 d + 6.9

e x t re m e f (x, y) = 3 x^{2} + 3 y^{2} - 6 x + 12 y