extreme f(x)=(8x)^3-(5x)^2-3x

Lösung

extrempunkte

f (x) = (8 x)^{3} - (5 x)^{2} - 3 x

Maximum (\frac{25 - 5233}{1536}, \frac{5233 5233 - 188425}{3538944}), Minimum (\frac{25 + 5233}{1536}, \frac{- 188425 - 5233 5233}{3538944})

Schritte zur Lösung

f^{'} (x) = 1536 x^{2} - 50 x - 3

Intervalle finden:

Ansteigend

: - \infty < x < \frac{- 5233 + 25}{1536},

Absteigend

: \frac{- 5233 + 25}{1536} < x < \frac{5233 + 25}{1536},

Ansteigend

: \frac{5233 + 25}{1536} < x < \infty

Stecke

x = \frac{25 - 5233}{1536}

(8 x)^{3} - (5 x)^{2} - 3 x : \frac{5233 5233 - 188425}{3538944}

Maximum (\frac{25 - 5233}{1536}, \frac{5233 5233 - 188425}{3538944})

Stecke

x = \frac{25 + 5233}{1536}

(8 x)^{3} - (5 x)^{2} - 3 x : \frac{- 188425 - 5233 5233}{3538944}

Minimum (\frac{25 + 5233}{1536}, \frac{- 188425 - 5233 5233}{3538944})

Maximum (\frac{25 - 5233}{1536}, \frac{5233 5233 - 188425}{3538944}), Minimum (\frac{25 + 5233}{1536}, \frac{- 188425 - 5233 5233}{3538944})

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

e x t re m e g (x) = x^{3} - 3 x^{2} + 3

e x t re m e f (x, y) = x^{2} + x y + y^{2} - 3 x - 6 y + 1

e x t re m e f (x) = \frac{x ^{2}}{x ^{2} - 5}

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