extreme f(x)=x(25-37+2x)(37/2-x)

Lösung

extrempunkte

f (x) = x (25 - 37 + 2 x) (\frac{37}{2} - x)

Minimum (\frac{49 - 1069}{6}, \frac{19747 - 1069 1069}{54}), Maximum (\frac{49 + 1069}{6}, \frac{1069 1069 + 19747}{54})

Schritte zur Lösung

f^{'} (x) = - 6 x^{2} + 98 x - 222

Intervalle finden:

Absteigend

: - \infty < x < \frac{- 1069 + 49}{6},

Ansteigend

: \frac{- 1069 + 49}{6} < x < \frac{1069 + 49}{6},

Absteigend

: \frac{1069 + 49}{6} < x < \infty

Stecke

x = \frac{49 - 1069}{6}

x (25 - 37 + 2 x) (\frac{37}{2} - x) : \frac{19747 - 1069 1069}{54}

Minimum (\frac{49 - 1069}{6}, \frac{19747 - 1069 1069}{54})

Stecke

x = \frac{49 + 1069}{6}

x (25 - 37 + 2 x) (\frac{37}{2} - x) : \frac{1069 1069 + 19747}{54}

Maximum (\frac{49 + 1069}{6}, \frac{1069 1069 + 19747}{54})

Minimum (\frac{49 - 1069}{6}, \frac{19747 - 1069 1069}{54}), Maximum (\frac{49 + 1069}{6}, \frac{1069 1069 + 19747}{54})

e x t re m e x^{3} - 6 x^{2} + 9 x + 7

e x t re m e x^{2} + x y - y^{2}

e x t re m e f (x) = \frac{1}{3} x^{3} - 3 x^{2} + 5 x

e x t re m e f (u, v) = 3 u - 7 v

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