inflection f(x)=x^4-16x^2

Lösung

wendepunkte

f (x) = x^{4} - 16 x^{2}

(- \frac{2 2}{3}, - \frac{320}{9}), (\frac{2 2}{3}, - \frac{320}{9})

Schritte zur Lösung

f^{''} (x) = 12 x^{2} - 32

Intervalle finden:

Konkav steigend

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

Konkav fallend

: - \frac{2 2}{3} < x < \frac{2 2}{3},

Konkav steigend

: \frac{2 2}{3} < x < \infty

Stecke

x = - \frac{2 2}{3}

x^{4} - 16 x^{2} : - \frac{320}{9}

(- \frac{2 2}{3}, - \frac{320}{9})

Stecke

x = \frac{2 2}{3}

x^{4} - 16 x^{2} : - \frac{320}{9}

(\frac{2 2}{3}, - \frac{320}{9})

(- \frac{2 2}{3}, - \frac{320}{9}), (\frac{2 2}{3}, - \frac{320}{9})

s im pl i f y \frac{x}{x}

in v erse f (x) = lo g_{\frac{1}{9}} (x)

in v erse f (x) = - \frac{1}{2} x + 10

sy mm e t ry x = 2

in v erse f (x) = 3 x + 5