What is the inflection f(x)=(x^2)/(4x^2+7) ?

The inflection f(x)=(x^2)/(4x^2+7) is (-(sqrt(7))/(2sqrt(3)), 1/16),((sqrt(7))/(2sqrt(3)), 1/16)

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inflection f(x)=(x^2)/(4x^2+7)

inflection points

f (x) = \frac{x ^{2}}{4 x ^{2} + 7}

(- \frac{7}{2 3}, \frac{1}{16}), (\frac{7}{2 3}, \frac{1}{16})

Solution steps

f^{''} (x) = \frac{14 ( 7 - 12 x ^{2} )}{( 4 x ^{2} + 7 ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - \frac{7}{2 3},

Concave Upward

: - \frac{7}{2 3} < x < \frac{7}{2 3},

Concave Downward

: \frac{7}{2 3} < x < \infty

Plug

x = - \frac{7}{2 3}

into

\frac{x ^{2}}{4 x ^{2} + 7} : \frac{1}{16}

(- \frac{7}{2 3}, \frac{1}{16})

Plug

x = \frac{7}{2 3}

into

\frac{x ^{2}}{4 x ^{2} + 7} : \frac{1}{16}

(\frac{7}{2 3}, \frac{1}{16})

(- \frac{7}{2 3}, \frac{1}{16}), (\frac{7}{2 3}, \frac{1}{16})

\frac{x ^{5}}{36 - x ^{2}}

f (x) = x^{2} + 3 x + 4

f (x) = x^{2} + 6 x - 16

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

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

What is the inflection f(x)=(x^2)/(4x^2+7) ?
The inflection f(x)=(x^2)/(4x^2+7) is (-(sqrt(7))/(2sqrt(3)), 1/16),((sqrt(7))/(2sqrt(3)), 1/16)