What is the inflection f(x)=(x^2)/(2x^2+3) ?

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

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inflection f(x)=(x^2)/(2x^2+3)

inflection points

f (x) = \frac{x ^{2}}{2 x ^{2} + 3}

(- \frac{1}{2}, \frac{1}{8}), (\frac{1}{2}, \frac{1}{8})

Solution steps

f^{''} (x) = \frac{18 ( - 2 x ^{2} + 1 )}{( 2 x ^{2} + 3 ) ^{3}}

Find intervals:

Concave Downward

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

Concave Upward

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

Concave Downward

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

Plug

x = - \frac{1}{2}

into

\frac{x ^{2}}{2 x ^{2} + 3} : \frac{1}{8}

(- \frac{1}{2}, \frac{1}{8})

Plug

x = \frac{1}{2}

into

\frac{x ^{2}}{2 x ^{2} + 3} : \frac{1}{8}

(\frac{1}{2}, \frac{1}{8})

(- \frac{1}{2}, \frac{1}{8}), (\frac{1}{2}, \frac{1}{8})

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