inflection 6x^4+2x^3-12x^2+3

Lösung

wendepunkte

6 x^{4} + 2 x^{3} - 12 x^{2} + 3

(- \frac{2}{3}, - \frac{47}{27}), (\frac{1}{2}, \frac{5}{8})

Schritte zur Lösung

f^{''} (x) = 72 x^{2} + 12 x - 24

Intervalle finden:

Konkav steigend

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

Konkav fallend

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

Konkav steigend

: \frac{1}{2} < x < \infty

Stecke

x = - \frac{2}{3}

6 x^{4} + 2 x^{3} - 12 x^{2} + 3 : - \frac{47}{27}

(- \frac{2}{3}, - \frac{47}{27})

Stecke

x = \frac{1}{2}

6 x^{4} + 2 x^{3} - 12 x^{2} + 3 : \frac{5}{8}

(\frac{1}{2}, \frac{5}{8})

(- \frac{2}{3}, - \frac{47}{27}), (\frac{1}{2}, \frac{5}{8})

d o main (x + 3)^{2}

a sy m pt o t es f (x) = \frac{8 x ^{2} + 1}{2 x ^{2} + 3 x - 2}

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

d o main 5 + x + 5

d o main f (x) = 5 x - 9