extreme x^3+8x^2-6x-4

Lösung

extrempunkte

x^{3} + 8 x^{2} - 6 x - 4

Maximum (- \frac{8 + 82}{3}, \frac{1024 + 110 82}{27} + 12 + 282), Minimum (\frac{- 8 + 82}{3}, \frac{1024 - 110 82}{27} + 12 - 282)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} + 16 x - 6

Intervalle finden:

Ansteigend

: - \infty < x < \frac{- 82 - 8}{3},

Absteigend

: \frac{- 82 - 8}{3} < x < \frac{82 - 8}{3},

Ansteigend

: \frac{82 - 8}{3} < x < \infty

Stecke

x = - \frac{8 + 82}{3}

x^{3} + 8 x^{2} - 6 x - 4 : \frac{1024 + 110 82}{27} + 12 + 282

Maximum (- \frac{8 + 82}{3}, \frac{1024 + 110 82}{27} + 12 + 282)

Stecke

x = \frac{- 8 + 82}{3}

x^{3} + 8 x^{2} - 6 x - 4 : \frac{1024 - 110 82}{27} + 12 - 282

Minimum (\frac{- 8 + 82}{3}, \frac{1024 - 110 82}{27} + 12 - 282)

Maximum (- \frac{8 + 82}{3}, \frac{1024 + 110 82}{27} + 12 + 282), Minimum (\frac{- 8 + 82}{3}, \frac{1024 - 110 82}{27} + 12 - 282)

e x t re m e f (x) = - \frac{13}{9} x^{2} + \frac{8}{3} x^{2} + \frac{37}{10}

e x t re m e \frac{( x - 4 )}{x ^{2}}

e x t re m e f (x) = \frac{2 x - 6}{x ^{2} + 7 - 4}

e x t re m e f (x) = (5 + x) + (1000 + 100 x)

e x t re m e f (x) = - (\frac{x}{3})^{3} + 2 x^{2} + 12 x + 1