What is the inflection f(x)= x/(x^2+25) ?

The inflection f(x)= x/(x^2+25) is (-5sqrt(3),-(sqrt(3))/(20)),(0,0),(5sqrt(3),(sqrt(3))/(20))

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inflection f(x)= x/(x^2+25)

inflection points

f (x) = \frac{x}{x ^{2} + 25}

(- 53, - \frac{3}{20}), (0, 0), (53, \frac{3}{20})

Solution steps

f^{''} (x) = - \frac{2 x ( - x ^{2} + 75 )}{( x ^{2} + 25 ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - 53,

Concave Upward

: - 53 < x < 0,

Concave Downward

: 0 < x < 53,

Concave Upward

: 53 < x < \infty

Plug

x = - 53

into

\frac{x}{x ^{2} + 25} : - \frac{3}{20}

(- 53, - \frac{3}{20})

Plug

x = 0

into

\frac{x}{x ^{2} + 25} : 0

(0, 0)

Plug

x = 53

into

\frac{x}{x ^{2} + 25} : \frac{3}{20}

(53, \frac{3}{20})

(- 53, - \frac{3}{20}), (0, 0), (53, \frac{3}{20})

What is the inflection f(x)= x/(x^2+25) ?
The inflection f(x)= x/(x^2+25) is (-5sqrt(3),-(sqrt(3))/(20)),(0,0),(5sqrt(3),(sqrt(3))/(20))