### Home > CALC > Chapter 9 > Lesson 9.1.2 > Problem9-30

9-30.

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 $f^{\prime\prime}(x) < 0$.