What is the inflection f(x)= x/(x^2+9) ?

The inflection f(x)= x/(x^2+9) is (-3sqrt(3),-1/(4sqrt(3))),(0,0),(3sqrt(3), 1/(4sqrt(3)))

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inflection f(x)= x/(x^2+9)

inflection points

f (x) = \frac{x}{x ^{2} + 9}

(- 33, - \frac{1}{4 3}), (0, 0), (33, \frac{1}{4 3})

Solution steps

f^{''} (x) = - \frac{2 x ( - x ^{2} + 27 )}{( x ^{2} + 9 ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - 33,

Concave Upward

: - 33 < x < 0,

Concave Downward

: 0 < x < 33,

Concave Upward

: 33 < x < \infty

Plug

x = - 33

into

\frac{x}{x ^{2} + 9} : - \frac{1}{4 3}

(- 33, - \frac{1}{4 3})

Plug

x = 0

into

\frac{x}{x ^{2} + 9} : 0

(0, 0)

Plug

x = 33

into

\frac{x}{x ^{2} + 9} : \frac{1}{4 3}

(33, \frac{1}{4 3})

(- 33, - \frac{1}{4 3}), (0, 0), (33, \frac{1}{4 3})

What is the inflection f(x)= x/(x^2+9) ?
The inflection f(x)= x/(x^2+9) is (-3sqrt(3),-1/(4sqrt(3))),(0,0),(3sqrt(3), 1/(4sqrt(3)))