inflection f(x)=3x^4-4x^3-5x^2

Lösung

wendepunkte

f (x) = 3 x^{4} - 4 x^{3} - 5 x^{2}

(\frac{2 - 14}{6}, \frac{76 14 - 317}{108}), (\frac{2 + 14}{6}, - \frac{317 + 76 14}{108})

Schritte zur Lösung

f^{''} (x) = 36 x^{2} - 24 x - 10

Intervalle finden:

Konkav steigend

: - \infty < x < - \frac{7}{3 2} + \frac{1}{3},

Konkav fallend

: - \frac{7}{3 2} + \frac{1}{3} < x < \frac{7}{3 2} + \frac{1}{3},

Konkav steigend

: \frac{7}{3 2} + \frac{1}{3} < x < \infty

Stecke

x = \frac{2 - 14}{6}

3 x^{4} - 4 x^{3} - 5 x^{2} : \frac{76 14 - 317}{108}

(\frac{2 - 14}{6}, \frac{76 14 - 317}{108})

Stecke

x = \frac{2 + 14}{6}

3 x^{4} - 4 x^{3} - 5 x^{2} : - \frac{317 + 76 14}{108}

(\frac{2 + 14}{6}, - \frac{317 + 76 14}{108})

(\frac{2 - 14}{6}, \frac{76 14 - 317}{108}), (\frac{2 + 14}{6}, - \frac{317 + 76 14}{108})

p a r i t y f (x) = \frac{x}{x ^{2} - 7}

d o main \frac{x}{x ^{2} - 4}

in v erse f (x) = \frac{1}{4} x - 5

in v erse f (x) = lo g_{4} (x) + 10

r an g e x^{3} - 2 x^{2} + \frac{1}{2}