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

The inflection f(x)= 1/(3x^2+8) is (-(2sqrt(2))/3 , 3/32),((2sqrt(2))/3 , 3/32)

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inflection f(x)= 1/(3x^2+8)

inflection points

f (x) = \frac{1}{3 x ^{2} + 8}

(- \frac{2 2}{3}, \frac{3}{32}), (\frac{2 2}{3}, \frac{3}{32})

Solution steps

f^{''} (x) = - \frac{6 ( 8 - 9 x ^{2} )}{( 3 x ^{2} + 8 ) ^{3}}

Find intervals:

Concave Upward

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

Concave Downward

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

Concave Upward

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

Plug

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

into

\frac{1}{3 x ^{2} + 8} : \frac{3}{32}

(- \frac{2 2}{3}, \frac{3}{32})

Plug

x = \frac{2 2}{3}

into

\frac{1}{3 x ^{2} + 8} : \frac{3}{32}

(\frac{2 2}{3}, \frac{3}{32})

(- \frac{2 2}{3}, \frac{3}{32}), (\frac{2 2}{3}, \frac{3}{32})

What is the inflection f(x)= 1/(3x^2+8) ?
The inflection f(x)= 1/(3x^2+8) is (-(2sqrt(2))/3 , 3/32),((2sqrt(2))/3 , 3/32)