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

The inflection 2x^2-1/(x^2) is (-\sqrt[4]{3/2},sqrt(6)-sqrt(2/3)),(\sqrt[4]{3/2},sqrt(6)-sqrt(2/3))

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

inflection points

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

(- 4 \frac{3}{2}, 6 - \frac{2}{3}), (4 \frac{3}{2}, 6 - \frac{2}{3})

Solution steps

f^{''} (x) = 4 - \frac{6}{x ^{4}}

Find intervals:

Concave Upward

: - \infty < x < - 4 \frac{3}{2},

Concave Downward

: - 4 \frac{3}{2} < x < 0,

Concave Downward

: 0 < x < 4 \frac{3}{2},

Concave Upward

: 4 \frac{3}{2} < x < \infty

Plug

x = - 4 \frac{3}{2}

into

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

(- 4 \frac{3}{2}, 6 - \frac{2}{3})

Plug

x = 4 \frac{3}{2}

into

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

(4 \frac{3}{2}, 6 - \frac{2}{3})

(- 4 \frac{3}{2}, 6 - \frac{2}{3}), (4 \frac{3}{2}, 6 - \frac{2}{3})

e x t re m e (x^{2} - 1)^{\frac{2}{3}}

s l o p e in t erce pt 4 x + 2 y = 7

s l o p e in t erce pt 7 x - y = - 3

d o main f (x) = \frac{7}{x + 6}

in f l ec t i o n tan (3 x - 5)

What is the inflection 2x^2-1/(x^2) ?
The inflection 2x^2-1/(x^2) is (-\sqrt[4]{3/2},sqrt(6)-sqrt(2/3)),(\sqrt[4]{3/2},sqrt(6)-sqrt(2/3))