What is the inflection (x^2)/(6x^2+4) ?

The inflection (x^2)/(6x^2+4) is (-(sqrt(2))/3 , 1/24),((sqrt(2))/3 , 1/24)

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inflection (x^2)/(6x^2+4)

inflection points

\frac{x ^{2}}{6 x ^{2} + 4}

(- \frac{2}{3}, \frac{1}{24}), (\frac{2}{3}, \frac{1}{24})

Solution steps

f^{''} (x) = \frac{2 ( 2 - 9 x ^{2} )}{( 3 x ^{2} + 2 ) ^{3}}

Find intervals:

Concave Downward

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

Concave Upward

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

Concave Downward

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

Plug

x = - \frac{2}{3}

into

\frac{x ^{2}}{6 x ^{2} + 4} : \frac{1}{24}

(- \frac{2}{3}, \frac{1}{24})

Plug

x = \frac{2}{3}

into

\frac{x ^{2}}{6 x ^{2} + 4} : \frac{1}{24}

(\frac{2}{3}, \frac{1}{24})

(- \frac{2}{3}, \frac{1}{24}), (\frac{2}{3}, \frac{1}{24})

f (x) = \frac{5 - x}{x ( x - 4 )}

g (x) = x^{2} - 3

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

(1, 0), (0, - 1)

(- 1, - 9), (4, - 7)

What is the inflection (x^2)/(6x^2+4) ?
The inflection (x^2)/(6x^2+4) is (-(sqrt(2))/3 , 1/24),((sqrt(2))/3 , 1/24)