Question 50
Let $I$ be the set of points $(x, y)$ in the Cartesian plane such that
$$
x \gt \left( \frac{y^{4}}{9} + 2015 \right)^{1/4}
$$
Let $f(r)$ denote the area of the intersection of $I$ and the disk $x^{2} + y^{2} \leq r^{2}$ of radius $r \gt 0$ centered at the origin $(0,0)$. Determine the minimum possible real number $L$ such that $f(r) \lt L r^{2}$ for all $r \gt 0$.
$$
x \gt \left( \frac{y^{4}}{9} + 2015 \right)^{1/4}
$$
Let $f(r)$ denote the area of the intersection of $I$ and the disk $x^{2} + y^{2} \leq r^{2}$ of radius $r \gt 0$ centered at the origin $(0,0)$. Determine the minimum possible real number $L$ such that $f(r) \lt L r^{2}$ for all $r \gt 0$.