What is the inflection x/(x^2+243) ?

The inflection x/(x^2+243) is (-27,-1/36),(0,0),(27, 1/36)

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inflection x/(x^2+243)

inflection

(- 27, - \frac{1}{36}), (0, 0), (27, \frac{1}{36})

Solution steps

f^{''} (x) = - \frac{2 x ( - x ^{2} + 729 )}{( x ^{2} + 243 ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - 27,

Concave Upward

: - 27 < x < 0,

Concave Downward

: 0 < x < 27,

Concave Upward

: 27 < x < \infty

Plug

x = - 27

into

\frac{x}{x ^{2} + 243} : - \frac{1}{36}

(- 27, - \frac{1}{36})

Plug

x = 0

into

\frac{x}{x ^{2} + 243} : 0

(0, 0)

Plug

x = 27

into

\frac{x}{x ^{2} + 243} : \frac{1}{36}

(27, \frac{1}{36})

(- 27, - \frac{1}{36}), (0, 0), (27, \frac{1}{36})

What is the inflection x/(x^2+243) ?
The inflection x/(x^2+243) is (-27,-1/36),(0,0),(27, 1/36)