Brittany and Kylie were trying to decide where the graph of $f(x) = \frac { 1 } { x ^ { 2 } }$ was concave up and where it was concave down. They both agreed that it was concave up for $x \lt 0$, but Kylie said that it could not be concave up for $x \gt 0$ since the function was decreasing. Brittany said that it did not matter; all that mattered was that it curved up. Which of the two was right? Explain your answer.