What is the inflection f(x)= x/(x^2+49) ?

The inflection f(x)= x/(x^2+49) is (-7sqrt(3),-(sqrt(3))/(28)),(0,0),(7sqrt(3),(sqrt(3))/(28))

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inflection f(x)= x/(x^2+49)

inflection points

f (x) = \frac{x}{x ^{2} + 49}

(- 73, - \frac{3}{28}), (0, 0), (73, \frac{3}{28})

Solution steps

f^{''} (x) = - \frac{2 x ( - x ^{2} + 147 )}{( x ^{2} + 49 ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - 73,

Concave Upward

: - 73 < x < 0,

Concave Downward

: 0 < x < 73,

Concave Upward

: 73 < x < \infty

Plug

x = - 73

into

\frac{x}{x ^{2} + 49} : - \frac{3}{28}

(- 73, - \frac{3}{28})

Plug

x = 0

into

\frac{x}{x ^{2} + 49} : 0

(0, 0)

Plug

x = 73

into

\frac{x}{x ^{2} + 49} : \frac{3}{28}

(73, \frac{3}{28})

(- 73, - \frac{3}{28}), (0, 0), (73, \frac{3}{28})

f (x) = - x^{3} + 9 x^{2}

f (x) = x^{2} + x + 2

f (x) = x^{5} = 2 x^{3} = x - 1

\frac{x + 8}{x - 4}

What is the inflection f(x)= x/(x^2+49) ?
The inflection f(x)= x/(x^2+49) is (-7sqrt(3),-(sqrt(3))/(28)),(0,0),(7sqrt(3),(sqrt(3))/(28))