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

Lösung

wendepunkte

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

(- \frac{2}{3}, - \frac{20}{9}), (\frac{2}{3}, - \frac{20}{9})

Schritte zur Lösung

f^{''} (x) = 12 x^{2} - 8

Intervalle finden:

Konkav steigend

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

Konkav fallend

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

Konkav steigend

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

Stecke

x = - \frac{2}{3}

x^{4} - 4 x^{2} : - \frac{20}{9}

(- \frac{2}{3}, - \frac{20}{9})

Stecke

x = \frac{2}{3}

x^{4} - 4 x^{2} : - \frac{20}{9}

(\frac{2}{3}, - \frac{20}{9})

(- \frac{2}{3}, - \frac{20}{9}), (\frac{2}{3}, - \frac{20}{9})

mi d p o in t (- 1, 7), (6, - 2)

a sy m pt o t es f (x) = \frac{x + 4}{- 2 x - 6}

in t erce pt s f (x) = x^{3} + 2 x^{2} - x - 2

r an g e lo g_{10} (x^{2} - 4)

a sy m pt o t es f (x) = \frac{c}{x}