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

The inflection 1+1/x-2/(x^3) is (-2sqrt(3),-5/(12sqrt(3))+1),(2sqrt(3), 5/(12sqrt(3))+1)

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

inflection points

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

(- 23, - \frac{5}{12 3} + 1), (23, \frac{5}{12 3} + 1)

Solution steps

f^{''} (x) = - \frac{24}{x ^{5}} + \frac{2}{x ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - 23,

Concave Upward

: - 23 < x < 0,

Concave Downward

: 0 < x < 23,

Concave Upward

: 23 < x < \infty

Plug

x = - 23

into

1 + \frac{1}{x} - \frac{2}{x ^{3}} : - \frac{5}{12 3} + 1

(- 23, - \frac{5}{12 3} + 1)

Plug

x = 23

into

1 + \frac{1}{x} - \frac{2}{x ^{3}} : \frac{5}{12 3} + 1

(23, \frac{5}{12 3} + 1)

(- 23, - \frac{5}{12 3} + 1), (23, \frac{5}{12 3} + 1)

x^{3} - 23.47 x^{2} + 223.6

r (x) = \frac{2 x - 3}{x ^{2} + x + 1}

\frac{x ^{2} + 10 x + 24}{x - 6}

2 cos (x)

\frac{9}{4} x - 5

What is the inflection 1+1/x-2/(x^3) ?
The inflection 1+1/x-2/(x^3) is (-2sqrt(3),-5/(12sqrt(3))+1),(2sqrt(3), 5/(12sqrt(3))+1)