extreme f(x)=x(21-37+2x)(37/2-x)

Lösung

extrempunkte

f (x) = x (21 - 37 + 2 x) (\frac{37}{2} - x)

Minimum (\frac{53 - 1033}{6}, \frac{7685 - 1033 1033}{54}), Maximum (\frac{53 + 1033}{6}, \frac{1033 1033 + 7685}{54})

Schritte zur Lösung

f^{'} (x) = - 6 x^{2} + 106 x - 296

Intervalle finden:

Absteigend

: - \infty < x < \frac{- 1033 + 53}{6},

Ansteigend

: \frac{- 1033 + 53}{6} < x < \frac{1033 + 53}{6},

Absteigend

: \frac{1033 + 53}{6} < x < \infty

Stecke

x = \frac{53 - 1033}{6}

x (21 - 37 + 2 x) (\frac{37}{2} - x) : \frac{7685 - 1033 1033}{54}

Minimum (\frac{53 - 1033}{6}, \frac{7685 - 1033 1033}{54})

Stecke

x = \frac{53 + 1033}{6}

x (21 - 37 + 2 x) (\frac{37}{2} - x) : \frac{1033 1033 + 7685}{54}

Maximum (\frac{53 + 1033}{6}, \frac{1033 1033 + 7685}{54})

Minimum (\frac{53 - 1033}{6}, \frac{7685 - 1033 1033}{54}), Maximum (\frac{53 + 1033}{6}, \frac{1033 1033 + 7685}{54})

e x t re m e f (x) = 4 x^{4} - 2 x^{3} - 7 x^{2} + 3 x + 1

e x t re m e f (x) = x^{3} + 10 x + 21

e x t re m e \frac{2 x}{3} - 17

e x t re m e y = \frac{3 x}{x ^{2} - 16}

e x t re m e y = - x + 2 cos (x)