What is the inflection f(x)=(-1)/(x^2+5) ?

The inflection f(x)=(-1)/(x^2+5) is (-sqrt(5/3),-3/20),(sqrt(5/3),-3/20)

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inflection f(x)=(-1)/(x^2+5)

inflection points

f (x) = \frac{- 1}{x ^{2} + 5}

(- \frac{5}{3}, - \frac{3}{20}), (\frac{5}{3}, - \frac{3}{20})

Solution steps

f^{''} (x) = \frac{2 ( - 3 x ^{2} + 5 )}{( x ^{2} + 5 ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - \frac{5}{3},

Concave Upward

: - \frac{5}{3} < x < \frac{5}{3},

Concave Downward

: \frac{5}{3} < x < \infty

Plug

x = - \frac{5}{3}

into

\frac{- 1}{x ^{2} + 5} : - \frac{3}{20}

(- \frac{5}{3}, - \frac{3}{20})

Plug

x = \frac{5}{3}

into

\frac{- 1}{x ^{2} + 5} : - \frac{3}{20}

(\frac{5}{3}, - \frac{3}{20})

(- \frac{5}{3}, - \frac{3}{20}), (\frac{5}{3}, - \frac{3}{20})

What is the inflection f(x)=(-1)/(x^2+5) ?
The inflection f(x)=(-1)/(x^2+5) is (-sqrt(5/3),-3/20),(sqrt(5/3),-3/20)