inflection 1/4 x^4-2x^2

Lösung

wendepunkte

\frac{1}{4} x^{4} - 2 x^{2}

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

Schritte zur Lösung

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

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}

\frac{1}{4} x^{4} - 2 x^{2} : - \frac{20}{9}

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

Stecke

x = \frac{2}{3}

\frac{1}{4} x^{4} - 2 x^{2} : - \frac{20}{9}

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

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

d o main f (x) = \frac{x + 5}{x ^{2} - 9}

in v erse f (x) = (x - 1)^{2} + 5

in t erce pt s y = x^{2}

in f l ec t i o n f (x) = - 2 x^{6} + 15 x^{5}

d o main \frac{x - 3}{4 + 5 x}