inflection 3x^4-24x^3+30x^2

Lösung

wendepunkte

3 x^{4} - 24 x^{3} + 30 x^{2}

(\frac{6 - 21}{3}, 10 (19 - 421) + \frac{192 21 - 887}{3}), (\frac{6 + 21}{3}, 10 (19 + 421) - \frac{887 + 192 21}{3})

Schritte zur Lösung

f^{''} (x) = 36 x^{2} - 144 x + 60

Intervalle finden:

Konkav steigend

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

Konkav fallend

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

Konkav steigend

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

Stecke

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

3 x^{4} - 24 x^{3} + 30 x^{2} : 10 (19 - 421) + \frac{192 21 - 887}{3}

(\frac{6 - 21}{3}, 10 (19 - 421) + \frac{192 21 - 887}{3})

Stecke

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

3 x^{4} - 24 x^{3} + 30 x^{2} : 10 (19 + 421) - \frac{887 + 192 21}{3}

(\frac{6 + 21}{3}, 10 (19 + 421) - \frac{887 + 192 21}{3})

(\frac{6 - 21}{3}, 10 (19 - 421) + \frac{192 21 - 887}{3}), (\frac{6 + 21}{3}, 10 (19 + 421) - \frac{887 + 192 21}{3})

in v erse f (x) = (x)^{4}

d o main f (x) = 2 - 13 - e^{4 t}

in v erse f (x) = x^{2}, x \geq 0

cr i t i c a l ln (4) + ln (x)

in t erce pt s f (x) = 2 x^{2} - 4 x - 6