extreme f(x)= 4/3 x^3-13/2 x^2-3x+11

Lösung

extrempunkte

f (x) = \frac{4}{3} x^{3} - \frac{13}{2} x^{2} - 3 x + 11

Maximum (\frac{13 - 217}{8}, \frac{217 217 - 3133}{192} + 11), Minimum (\frac{13 + 217}{8}, \frac{- 3133 - 217 217}{192} + 11)

Schritte zur Lösung

f^{'} (x) = 4 x^{2} - 13 x - 3

Intervalle finden:

Ansteigend

: - \infty < x < \frac{- 217 + 13}{8},

Absteigend

: \frac{- 217 + 13}{8} < x < \frac{217 + 13}{8},

Ansteigend

: \frac{217 + 13}{8} < x < \infty

Stecke

x = \frac{13 - 217}{8}

\frac{4}{3} x^{3} - \frac{13}{2} x^{2} - 3 x + 11 : \frac{217 217 - 3133}{192} + 11

Maximum (\frac{13 - 217}{8}, \frac{217 217 - 3133}{192} + 11)

Stecke

x = \frac{13 + 217}{8}

\frac{4}{3} x^{3} - \frac{13}{2} x^{2} - 3 x + 11 : \frac{- 3133 - 217 217}{192} + 11

Minimum (\frac{13 + 217}{8}, \frac{- 3133 - 217 217}{192} + 11)

Maximum (\frac{13 - 217}{8}, \frac{217 217 - 3133}{192} + 11), Minimum (\frac{13 + 217}{8}, \frac{- 3133 - 217 217}{192} + 11)

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

e x t re m e f (x) = 8 x - 16 cos (x)

e x t re m e f (x, y) = x^{2} + x y + y^{2} - 9

e x t re m e f (x) = x y + y - 11 x

e x t re m e 3 cos^{2} (x)