Solution
= Solution
A point $x\in X$ is a <critical point of a smooth map> if $df_x:T_xX\to T_{f(x)}Y$ is not surjective. A <critical value> is the image of at least one critical point. A <regular value> is a point $y\in Y$ for which every point of $f^{-1}(y)$ has surjective <differential>. A point outside the image is therefore a <regular value> vacuously. These definitions use rank relative to $\dim Y$, not merely whether a <derivative> vanishes in chosen coordinates.