The Rightmost Bend

Consider the rational function

$f(x) = \frac{x}{x^2 + 3}$

The denominator is never zero, so $f$ is defined and smooth for every real $x$.

This curve does not just bend one way. Its concavity genuinely flips sign at more than one point.

Task: find the inflection point with the largest $x$-value, and report its $y$-coordinate — the value of $f$ there, not the $x$ where it happens.

Round your answer to two decimal places.