extreme f(x)=x(17-43+2x)(43/2-x)

Lösung

extrempunkte

f (x) = x (17 - 43 + 2 x) (\frac{43}{2} - x)

Minimum (\frac{69 - 1407}{6}, - \frac{6210 + 469 1407}{18}), Maximum (\frac{69 + 1407}{6}, \frac{469 1407 - 6210}{18})

Schritte zur Lösung

f^{'} (x) = - 6 x^{2} + 138 x - 559

Intervalle finden:

Absteigend

: - \infty < x < - \frac{469}{2 3} + \frac{23}{2},

Ansteigend

: - \frac{469}{2 3} + \frac{23}{2} < x < \frac{469}{2 3} + \frac{23}{2},

Absteigend

: \frac{469}{2 3} + \frac{23}{2} < x < \infty

Stecke

x = \frac{69 - 1407}{6}

x (17 - 43 + 2 x) (\frac{43}{2} - x) : - \frac{6210 + 469 1407}{18}

Minimum (\frac{69 - 1407}{6}, - \frac{6210 + 469 1407}{18})

Stecke

x = \frac{69 + 1407}{6}

x (17 - 43 + 2 x) (\frac{43}{2} - x) : \frac{469 1407 - 6210}{18}

Maximum (\frac{69 + 1407}{6}, \frac{469 1407 - 6210}{18})

Minimum (\frac{69 - 1407}{6}, - \frac{6210 + 469 1407}{18}), Maximum (\frac{69 + 1407}{6}, \frac{469 1407 - 6210}{18})

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

e x t re m e ln^{2} (x)

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

e x t re m e f (x) = \frac{x ^{3}}{x ^{2} - 64}

e x t re m e f (x) = 5 x^{3} - 5 x^{2} - 5 x + 7, - 1 \leq x \leq 2