What is the inflection (2x^2+3)/(x^2+1) ?

The inflection (2x^2+3)/(x^2+1) is (-1/(sqrt(3)), 11/4),(1/(sqrt(3)), 11/4)

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inflection (2x^2+3)/(x^2+1)

inflection points

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

(- \frac{1}{3}, \frac{11}{4}), (\frac{1}{3}, \frac{11}{4})

Solution steps

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

Find intervals:

Concave Upward

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

Concave Downward

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

Concave Upward

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

Plug

x = - \frac{1}{3}

into

\frac{2 x ^{2} + 3}{x ^{2} + 1} : \frac{11}{4}

(- \frac{1}{3}, \frac{11}{4})

Plug

x = \frac{1}{3}

into

\frac{2 x ^{2} + 3}{x ^{2} + 1} : \frac{11}{4}

(\frac{1}{3}, \frac{11}{4})

(- \frac{1}{3}, \frac{11}{4}), (\frac{1}{3}, \frac{11}{4})

y = - 2

f (x) = 3 x^{2} - 12 x + 4

X^{3}

f (x) = \frac{( 6 - 7 x )}{( 8 - 5 x )}

x (x + 1)

What is the inflection (2x^2+3)/(x^2+1) ?
The inflection (2x^2+3)/(x^2+1) is (-1/(sqrt(3)), 11/4),(1/(sqrt(3)), 11/4)