What is the inflection f(x)=ln(6+x^2) ?

The inflection f(x)=ln(6+x^2) is (-sqrt(6),ln(12)),(sqrt(6),ln(12))

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inflection f(x)=ln(6+x^2)

inflection

(- 6, ln (12)), (6, ln (12))

Solution steps

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

Find intervals:

Concave Downward

: - \infty < x < - 6,

Concave Upward

: - 6 < x < 6,

Concave Downward

: 6 < x < \infty

Plug

x = - 6

into

ln (6 + x^{2}) : ln (12)

(- 6, ln (12))

Plug

x = 6

into

ln (6 + x^{2}) : ln (12)

(6, ln (12))

(- 6, ln (12)), (6, ln (12))

What is the inflection f(x)=ln(6+x^2) ?
The inflection f(x)=ln(6+x^2) is (-sqrt(6),ln(12)),(sqrt(6),ln(12))