inflection f(x)=x^4-32x^2+1

Lösung

wendepunkte

f (x) = x^{4} - 32 x^{2} + 1

(- \frac{4}{3}, - \frac{1271}{9}), (\frac{4}{3}, - \frac{1271}{9})

Schritte zur Lösung

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

Intervalle finden:

Konkav steigend

: - \infty < x < - \frac{4}{3},

Konkav fallend

: - \frac{4}{3} < x < \frac{4}{3},

Konkav steigend

: \frac{4}{3} < x < \infty

Stecke

x = - \frac{4}{3}

x^{4} - 32 x^{2} + 1 : - \frac{1271}{9}

(- \frac{4}{3}, - \frac{1271}{9})

Stecke

x = \frac{4}{3}

x^{4} - 32 x^{2} + 1 : - \frac{1271}{9}

(\frac{4}{3}, - \frac{1271}{9})

(- \frac{4}{3}, - \frac{1271}{9}), (\frac{4}{3}, - \frac{1271}{9})

d o main (x + 4)^{3} - 2

p a r i t y \frac{1}{x ^{2}}

l in e (0, - 2), (- 4, 4)

e x t re m e f (x) = x^{4} - 128 x^{2} + 4096

cr i t i c a l f (x) = x^{2 x}