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

Lösung

wendepunkte

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

(- \frac{6 + 66}{6}, - \frac{893 + 108 66}{36}), (\frac{- 6 + 66}{6}, \frac{108 66 - 893}{36})

Schritte zur Lösung

f^{''} (x) = 12 y^{2} + 24 y - 10

Intervalle finden:

Konkav steigend

: - \infty < y < - \frac{11}{6} - 1,

Konkav fallend

: - \frac{11}{6} - 1 < y < \frac{11}{6} - 1,

Konkav steigend

: \frac{11}{6} - 1 < y < \infty

Stecke

y = - \frac{6 + 66}{6}

y^{4} + 4 y^{3} - 5 y^{2} : - \frac{893 + 108 66}{36}

(- \frac{6 + 66}{6}, - \frac{893 + 108 66}{36})

Stecke

y = \frac{- 6 + 66}{6}

y^{4} + 4 y^{3} - 5 y^{2} : \frac{108 66 - 893}{36}

(\frac{- 6 + 66}{6}, \frac{108 66 - 893}{36})

(- \frac{6 + 66}{6}, - \frac{893 + 108 66}{36}), (\frac{- 6 + 66}{6}, \frac{108 66 - 893}{36})

in v erse f (x) = \frac{3 x}{x - 8}

in v erse f (x) = - 3 x + 8

s l o p e 5 x + 2 y = 10

in v erse f (x) = \frac{21 - 7 x}{4 x}

in v erse f (x) = x^{2} - 6 x + 4