Square the answer

You nearly caught me.

The maximum value of $x$ is $3$ , that is, $x \in (-\infty,3]$

Notice that the smaller negative values will yield a larger value of $x^2$ .

Eg. $x=-4\implies x^2=16,\quad x=-100 \implies x^2=10000$

This implies that as long as the minimum value of $x$ is not stated, $\boxed{\text{There is no maximum value}}$

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Another way to look at it is let $f(x)=x^2$ with domain $D_f = (-\infty,3]$

For this domain, the range is found to be $R_f=[0,\infty)$ . $\boxed{\text{There is no maximum value}}$