extreme f(x)=x(20-39+2x)(39/2-x)

Lösung

extrempunkte

f (x) = x (20 - 39 + 2 x) (\frac{39}{2} - x)

Minimum (\frac{58 - 1141}{6}, \frac{1711 - 1141 1141}{54}), Maximum (\frac{58 + 1141}{6}, \frac{1141 1141 + 1711}{54})

Schritte zur Lösung

f^{'} (x) = - 6 x^{2} + 116 x - \frac{741}{2}

Intervalle finden:

Absteigend

: - \infty < x < - \frac{1141}{6} + \frac{29}{3},

Ansteigend

: - \frac{1141}{6} + \frac{29}{3} < x < \frac{1141}{6} + \frac{29}{3},

Absteigend

: \frac{1141}{6} + \frac{29}{3} < x < \infty

Stecke

x = \frac{58 - 1141}{6}

x (20 - 39 + 2 x) (\frac{39}{2} - x) : \frac{1711 - 1141 1141}{54}

Minimum (\frac{58 - 1141}{6}, \frac{1711 - 1141 1141}{54})

Stecke

x = \frac{58 + 1141}{6}

x (20 - 39 + 2 x) (\frac{39}{2} - x) : \frac{1141 1141 + 1711}{54}

Maximum (\frac{58 + 1141}{6}, \frac{1141 1141 + 1711}{54})

Minimum (\frac{58 - 1141}{6}, \frac{1711 - 1141 1141}{54}), Maximum (\frac{58 + 1141}{6}, \frac{1141 1141 + 1711}{54})

e x t re m e \frac{x ^{2} + 1}{x ^{2} - 9}

e x t re m e f (x) = \frac{x ^{2} - 6 x + 9}{x - 7}

e x t re m e f (x) = x 21 - x

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

e x t re m e f (x) = 2 x + 1 - x - 1