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

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

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

inflection

(- 1, \frac{1}{4}), (1, \frac{1}{4})

Solution steps

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

Find intervals:

Concave Downward

: - \infty < x < - 1,

Concave Upward

: - 1 < x < 1,

Concave Downward

: 1 < x < \infty

Plug

x = - 1

into

\frac{x ^{2}}{x ^{2} + 3} : \frac{1}{4}

(- 1, \frac{1}{4})

Plug

x = 1

into

\frac{x ^{2}}{x ^{2} + 3} : \frac{1}{4}

(1, \frac{1}{4})

(- 1, \frac{1}{4}), (1, \frac{1}{4})

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