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

The inflection (x^2-3)/(x^3) is (-3sqrt(2),-5/(18sqrt(2))),(3sqrt(2), 5/(18sqrt(2)))

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

inflection points

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

(- 32, - \frac{5}{18 2}), (32, \frac{5}{18 2})

Solution steps

f^{''} (x) = - \frac{2 ( - x ^{2} + 18 )}{x ^{5}}

Find intervals:

Concave Downward

: - \infty < x < - 32,

Concave Upward

: - 32 < x < 0,

Concave Downward

: 0 < x < 32,

Concave Upward

: 32 < x < \infty

Plug

x = - 32

into

\frac{x ^{2} - 3}{x ^{3}} : - \frac{5}{18 2}

(- 32, - \frac{5}{18 2})

Plug

x = 32

into

\frac{x ^{2} - 3}{x ^{3}} : \frac{5}{18 2}

(32, \frac{5}{18 2})

(- 32, - \frac{5}{18 2}), (32, \frac{5}{18 2})

f (x) = \frac{1}{x ^{2} - 4}

\frac{x ^{2} - 16}{4 x ^{2}}

x^{3} + x^{2} - 4 x - 4

f (x) = x^{2} + 2 x

y - 5 = - 2 (x + 5)

What is the inflection (x^2-3)/(x^3) ?
The inflection (x^2-3)/(x^3) is (-3sqrt(2),-5/(18sqrt(2))),(3sqrt(2), 5/(18sqrt(2)))