What is the inflection f(x)= x/(x^2+36) ?

The inflection f(x)= x/(x^2+36) is (-6sqrt(3),-1/(8sqrt(3))),(0,0),(6sqrt(3), 1/(8sqrt(3)))

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inflection f(x)= x/(x^2+36)

inflection points

f (x) = \frac{x}{x ^{2} + 36}

(- 63, - \frac{1}{8 3}), (0, 0), (63, \frac{1}{8 3})

Solution steps

f^{''} (x) = - \frac{2 x ( - x ^{2} + 108 )}{( x ^{2} + 36 ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - 63,

Concave Upward

: - 63 < x < 0,

Concave Downward

: 0 < x < 63,

Concave Upward

: 63 < x < \infty

Plug

x = - 63

into

\frac{x}{x ^{2} + 36} : - \frac{1}{8 3}

(- 63, - \frac{1}{8 3})

Plug

x = 0

into

\frac{x}{x ^{2} + 36} : 0

(0, 0)

Plug

x = 63

into

\frac{x}{x ^{2} + 36} : \frac{1}{8 3}

(63, \frac{1}{8 3})

(- 63, - \frac{1}{8 3}), (0, 0), (63, \frac{1}{8 3})

f (x) = 2 cos (3 x + 2)

f (x) = - 8 x + 240

y + 1 = \frac{2}{3} (x - 8)

(4, 1), (0, 3)

f (x) = \frac{e ^{x}}{x}

What is the inflection f(x)= x/(x^2+36) ?
The inflection f(x)= x/(x^2+36) is (-6sqrt(3),-1/(8sqrt(3))),(0,0),(6sqrt(3), 1/(8sqrt(3)))