What is the inflection (x^2-1)/(x^3) ?

The inflection (x^2-1)/(x^3) is (-sqrt(6),-5/(6sqrt(6))),(sqrt(6), 5/(6sqrt(6)))

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inflection (x^2-1)/(x^3)

inflection points

\frac{x ^{2} - 1}{x ^{3}}

(- 6, - \frac{5}{6 6}), (6, \frac{5}{6 6})

Solution steps

f^{''} (x) = - \frac{2 ( - x ^{2} + 6 )}{x ^{5}}

Find intervals:

Concave Downward

: - \infty < x < - 6,

Concave Upward

: - 6 < x < 0,

Concave Downward

: 0 < x < 6,

Concave Upward

: 6 < x < \infty

Plug

x = - 6

into

\frac{x ^{2} - 1}{x ^{3}} : - \frac{5}{6 6}

(- 6, - \frac{5}{6 6})

Plug

x = 6

into

\frac{x ^{2} - 1}{x ^{3}} : \frac{5}{6 6}

(6, \frac{5}{6 6})

(- 6, - \frac{5}{6 6}), (6, \frac{5}{6 6})

What is the inflection (x^2-1)/(x^3) ?
The inflection (x^2-1)/(x^3) is (-sqrt(6),-5/(6sqrt(6))),(sqrt(6), 5/(6sqrt(6)))