What is the inflection f(x)= x/(x^2+16) ?

The inflection f(x)= x/(x^2+16) is (-4sqrt(3),-(sqrt(3))/(16)),(0,0),(4sqrt(3),(sqrt(3))/(16))

inflection f(x)= x/(x^2+16)

inflection points

f (x) = \frac{x}{x ^{2} + 16}

(- 43, - \frac{3}{16}), (0, 0), (43, \frac{3}{16})

Solution steps

f^{''} (x) = - \frac{2 x ( - x ^{2} + 48 )}{( x ^{2} + 16 ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - 43,

Concave Upward

: - 43 < x < 0,

Concave Downward

: 0 < x < 43,

Concave Upward

: 43 < x < \infty

Plug

x = - 43

into

\frac{x}{x ^{2} + 16} : - \frac{3}{16}

(- 43, - \frac{3}{16})

Plug

x = 0

into

\frac{x}{x ^{2} + 16} : 0

(0, 0)

Plug

x = 43

into

\frac{x}{x ^{2} + 16} : \frac{3}{16}

(43, \frac{3}{16})

(- 43, - \frac{3}{16}), (0, 0), (43, \frac{3}{16})

d i s t an ce (3, - 7), (- 1, 2)

l in e m = - \frac{7}{6}, (- 6, - 2)

e x t re m e f (x) = - x^{4} + x^{3} + 2 x^{2}

in v erse f (x) = \frac{x + 1}{2 x + 3}

d o main f (x) = \frac{1}{x} - 4

What is the inflection f(x)= x/(x^2+16) ?
The inflection f(x)= x/(x^2+16) is (-4sqrt(3),-(sqrt(3))/(16)),(0,0),(4sqrt(3),(sqrt(3))/(16))