extreme 5x^3+67.5x^2+2x+10

Lösung

extrempunkte

5 x^{3} + 67.5 x^{2} + 2 x + 10

Maximum (\frac{- 135 - 18105}{30}, 1814.51483 \dots), Minimum (\frac{- 135 + 18105}{30}, 9.98516 \dots)

Schritte zur Lösung

f^{'} (x) = 15 x^{2} + 135 x + 2

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{1207}{2 15} - \frac{9}{2},

Absteigend

: - \frac{1207}{2 15} - \frac{9}{2} < x < \frac{1207}{2 15} - \frac{9}{2},

Ansteigend

: \frac{1207}{2 15} - \frac{9}{2} < x < \infty

Stecke

x = \frac{- 135 - 18105}{30}

5 x^{3} + 67.5 x^{2} + 2 x + 10 : 1814.51483 \dots

Maximum (\frac{- 135 - 18105}{30}, 1814.51483 \dots)

Stecke

x = \frac{- 135 + 18105}{30}

5 x^{3} + 67.5 x^{2} + 2 x + 10 : 9.98516 \dots

Minimum (\frac{- 135 + 18105}{30}, 9.98516 \dots)

Maximum (\frac{- 135 - 18105}{30}, 1814.51483 \dots), Minimum (\frac{- 135 + 18105}{30}, 9.98516 \dots)

e x t re m e f (x) = 25 x^{2} - x^{3}

e x t re m e f (x) = 4 x^{2} - 16 x + 20

e x t re m e g (x) = - 50 x^{2} + 400 x + 500

e x t re m e f (x) = 4 x + 5 y

e x t re m e x^{11} - 3 x^{9} + 2