extreme f(x)=x(7-2x)(9-2x)

Lösung

extrempunkte

f (x) = x (7 - 2 x) (9 - 2 x)

Maximum (\frac{16 - 67}{6}, \frac{440 + 67 67}{27}), Minimum (\frac{16 + 67}{6}, \frac{440 - 67 67}{27})

Schritte zur Lösung

f^{'} (x) = 12 x^{2} - 64 x + 63

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{67}{6} + \frac{8}{3},

Absteigend

: - \frac{67}{6} + \frac{8}{3} < x < \frac{67}{6} + \frac{8}{3},

Ansteigend

: \frac{67}{6} + \frac{8}{3} < x < \infty

Stecke

x = \frac{16 - 67}{6}

x (7 - 2 x) (9 - 2 x) : \frac{440 + 67 67}{27}

Maximum (\frac{16 - 67}{6}, \frac{440 + 67 67}{27})

Stecke

x = \frac{16 + 67}{6}

x (7 - 2 x) (9 - 2 x) : \frac{440 - 67 67}{27}

Minimum (\frac{16 + 67}{6}, \frac{440 - 67 67}{27})

Maximum (\frac{16 - 67}{6}, \frac{440 + 67 67}{27}), Minimum (\frac{16 + 67}{6}, \frac{440 - 67 67}{27})

h (x) = x + 3

s l o p e x = 8

e x t re m e f (x) = - 5 x^{3} - 6

l in e y = - \frac{1}{4} x - 10

d o main - x^{2} + 4 x + 12