What is the inflection f(x)=(x^2)/(8x^2+2) ?

The inflection f(x)=(x^2)/(8x^2+2) is (-1/(2sqrt(3)), 1/32),(1/(2sqrt(3)), 1/32)

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inflection f(x)=(x^2)/(8x^2+2)

inflection points

f (x) = \frac{x ^{2}}{8 x ^{2} + 2}

(- \frac{1}{2 3}, \frac{1}{32}), (\frac{1}{2 3}, \frac{1}{32})

Solution steps

f^{''} (x) = \frac{1 - 12 x ^{2}}{( 4 x ^{2} + 1 ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - \frac{1}{2 3},

Concave Upward

: - \frac{1}{2 3} < x < \frac{1}{2 3},

Concave Downward

: \frac{1}{2 3} < x < \infty

Plug

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

into

\frac{x ^{2}}{8 x ^{2} + 2} : \frac{1}{32}

(- \frac{1}{2 3}, \frac{1}{32})

Plug

x = \frac{1}{2 3}

into

\frac{x ^{2}}{8 x ^{2} + 2} : \frac{1}{32}

(\frac{1}{2 3}, \frac{1}{32})

(- \frac{1}{2 3}, \frac{1}{32}), (\frac{1}{2 3}, \frac{1}{32})

f (x) = x^{3} - 3 x^{2} - 9 x - 4

3 x^{2}

arcsin (tan (x))

f (x) = e^{x + 3} + 4

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

What is the inflection f(x)=(x^2)/(8x^2+2) ?
The inflection f(x)=(x^2)/(8x^2+2) is (-1/(2sqrt(3)), 1/32),(1/(2sqrt(3)), 1/32)