### Home > CALC3RD > Chapter Ch9 > Lesson 9.1.2 > Problem9-29

9-29.

No calculator! Find the interval(s) over which  $f(x)=\frac{2}{x^2+1}$ is concave down.

If you differentiate this function correctly, the second derivative is:

$f^{\prime\prime}(x)=\frac{4(3x^2-1)}{(x^2+1)^3}$

The graph of the function is concave down when $f^{\prime\prime}(x) < 0$.