inflection f(x)=(x-2)^2(x-4)^2

Lösung

wendepunkte

f (x) = (x - 2)^{2} (x - 4)^{2}

(\frac{9 - 3}{3}, - \frac{572}{9} + 64), (\frac{9 + 3}{3}, - \frac{572}{9} + 64)

Schritte zur Lösung

f^{''} (x) = 4 (3 x^{2} - 18 x + 26)

Intervalle finden:

Konkav steigend

: - \infty < x < - \frac{1}{3} + 3,

Konkav fallend

: - \frac{1}{3} + 3 < x < \frac{1}{3} + 3,

Konkav steigend

: \frac{1}{3} + 3 < x < \infty

Stecke

x = \frac{9 - 3}{3}

(x - 2)^{2} (x - 4)^{2} : - \frac{572}{9} + 64

(\frac{9 - 3}{3}, - \frac{572}{9} + 64)

Stecke

x = \frac{9 + 3}{3}

(x - 2)^{2} (x - 4)^{2} : - \frac{572}{9} + 64

(\frac{9 + 3}{3}, - \frac{572}{9} + 64)

(\frac{9 - 3}{3}, - \frac{572}{9} + 64), (\frac{9 + 3}{3}, - \frac{572}{9} + 64)

sy mm e t ry 6 x^{2} + 12 x - 1

d o main f (x) = 3 1 - x

d o main 5 + 8 x

in t erce pt s f (x) = x^{2} - 7 x - 18

in t erce pt s x^{3} - 4 x