inflection-x^4-2x^3+2x^2-5

Lösung

wendepunkte

- x^{4} - 2 x^{3} + 2 x^{2} - 5

(- \frac{3 + 21}{6}, \frac{43 + 9 21}{18} - 5), (\frac{21 - 3}{6}, \frac{43 - 9 21}{18} - 5)

Schritte zur Lösung

f^{''} (x) = - 12 x^{2} - 12 x + 4

Intervalle finden:

Konkav fallend

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

Konkav steigend

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

Konkav fallend

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

Stecke

x = - \frac{3 + 21}{6}

- x^{4} - 2 x^{3} + 2 x^{2} - 5 : \frac{43 + 9 21}{18} - 5

(- \frac{3 + 21}{6}, \frac{43 + 9 21}{18} - 5)

Stecke

x = \frac{21 - 3}{6}

- x^{4} - 2 x^{3} + 2 x^{2} - 5 : \frac{43 - 9 21}{18} - 5

(\frac{21 - 3}{6}, \frac{43 - 9 21}{18} - 5)

(- \frac{3 + 21}{6}, \frac{43 + 9 21}{18} - 5), (\frac{21 - 3}{6}, \frac{43 - 9 21}{18} - 5)

d o main f (x) = \frac{8 + 5 x}{x - 1}

cr i t i c a l f (x) = x^{\frac{2}{3}} (x - 4)

e x t re m e f (x) = 5 x^{5} - 50 x^{3} + 1600

d o main f (x) = \frac{x}{∣ x + 2 ∣ - 8}

d o main f (x) = \frac{1}{ln ( x )}