extreme f(x)=x(22-37+2x)(37/2-x)

Lösung

extrempunkte

f (x) = x (22 - 37 + 2 x) (\frac{37}{2} - x)

Minimum (\frac{52 - 1039}{6}, \frac{10738 - 1039 1039}{54}), Maximum (\frac{52 + 1039}{6}, \frac{1039 1039 + 10738}{54})

Schritte zur Lösung

f^{'} (x) = - 6 x^{2} + 104 x - \frac{555}{2}

Intervalle finden:

Absteigend

: - \infty < x < - \frac{1039}{6} + \frac{26}{3},

Ansteigend

: - \frac{1039}{6} + \frac{26}{3} < x < \frac{1039}{6} + \frac{26}{3},

Absteigend

: \frac{1039}{6} + \frac{26}{3} < x < \infty

Stecke

x = \frac{52 - 1039}{6}

x (22 - 37 + 2 x) (\frac{37}{2} - x) : \frac{10738 - 1039 1039}{54}

Minimum (\frac{52 - 1039}{6}, \frac{10738 - 1039 1039}{54})

Stecke

x = \frac{52 + 1039}{6}

x (22 - 37 + 2 x) (\frac{37}{2} - x) : \frac{1039 1039 + 10738}{54}

Maximum (\frac{52 + 1039}{6}, \frac{1039 1039 + 10738}{54})

Minimum (\frac{52 - 1039}{6}, \frac{10738 - 1039 1039}{54}), Maximum (\frac{52 + 1039}{6}, \frac{1039 1039 + 10738}{54})

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

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

e x t re m e (x + 1)^{2} (x - 2)

e x t re m e f (x) = x^{5} - 5 x^{4} + 5

e x t re m e f (x) = \frac{1}{4} x^{4} - 4 x^{2} + 2