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

Lösung

wendepunkte

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

(\frac{15 - 129}{48}, \frac{5 ( 293 - 27 129 )}{18432}), (\frac{15 + 129}{48}, \frac{5 ( 293 + 27 129 )}{18432})

Schritte zur Lösung

f^{''} (x) = - 48 x^{2} + 30 x - 2

Intervalle finden:

Konkav fallend

: - \infty < x < - \frac{43}{16 3} + \frac{5}{16},

Konkav steigend

: - \frac{43}{16 3} + \frac{5}{16} < x < \frac{43}{16 3} + \frac{5}{16},

Konkav fallend

: \frac{43}{16 3} + \frac{5}{16} < x < \infty

Stecke

x = \frac{15 - 129}{48}

- 4 x^{4} + 5 x^{3} - x^{2} : \frac{5 ( 293 - 27 129 )}{18432}

(\frac{15 - 129}{48}, \frac{5 ( 293 - 27 129 )}{18432})

Stecke

x = \frac{15 + 129}{48}

- 4 x^{4} + 5 x^{3} - x^{2} : \frac{5 ( 293 + 27 129 )}{18432}

(\frac{15 + 129}{48}, \frac{5 ( 293 + 27 129 )}{18432})

(\frac{15 - 129}{48}, \frac{5 ( 293 - 27 129 )}{18432}), (\frac{15 + 129}{48}, \frac{5 ( 293 + 27 129 )}{18432})

m o n o t o n e 5 x^{3} - 5 x^{2} - 4

p a r i t y f (x) = 8 x

d o main f (x) = 2 - 5 x

r an g e cos (4 x)

r an g e \frac{3 x}{2 x - 1}