Show that $\displaystyle f_n(x) = \frac{x}{1+n^2x^2}$ converges uniformly to $0$ on $[0, \infty)$

Question

Trying to use the definition of uniform convergence where $|f_n(x) \to f(x)| \to 0$ as $n \to$ ∞ but not sure how to apply this definition to the problem

Answer 1

Hint. Compute $\sup_x f_n(x)$ for each $n$, by finding the maximum of $f_n$ via its critical points, the roots of $f_n'$.