inflection (x-1)^4*(x-3)^2

Lösung

wendepunkte

(x - 1)^{4} \cdot (x - 3)^{2}

(\frac{35 - 2 10}{15}, \frac{3584 10 - 756893}{91125} + 9), (\frac{35 + 2 10}{15}, \frac{- 756893 - 3584 10}{91125} + 9)

Schritte zur Lösung

f^{''} (x) = 2 (3 (x - 1)^{2} (x - 3) (3 x - 7) + 2 (3 x - 8) (x - 1)^{3})

Intervalle finden:

Konkav steigend

: - \infty < x < 1,

Konkav steigend

: 1 < x < \frac{35 - 2 10}{15},

Konkav fallend

: \frac{35 - 2 10}{15} < x < \frac{35 + 2 10}{15},

Konkav steigend

: \frac{35 + 2 10}{15} < x < \infty

Stecke

x = \frac{35 - 2 10}{15}

(x - 1)^{4} \cdot (x - 3)^{2} : \frac{3584 10 - 756893}{91125} + 9

(\frac{35 - 2 10}{15}, \frac{3584 10 - 756893}{91125} + 9)

Stecke

x = \frac{35 + 2 10}{15}

(x - 1)^{4} \cdot (x - 3)^{2} : \frac{- 756893 - 3584 10}{91125} + 9

(\frac{35 + 2 10}{15}, \frac{- 756893 - 3584 10}{91125} + 9)

(\frac{35 - 2 10}{15}, \frac{3584 10 - 756893}{91125} + 9), (\frac{35 + 2 10}{15}, \frac{- 756893 - 3584 10}{91125} + 9)

a sy m pt o t es \frac{6 - 3 x}{x - 4}

a sy m pt o t es f (x) = \frac{5}{x ^{2} - 16}

l in e (0, 20), (13500, 4.5)

in v erse y = \frac{( x - 4 )}{( x + 1 )}

r an g e x^{3} - x