Let $M$ be a manifold and $C_0,C_1$ be two disjoint closed subsets of $M$ , then smooth Urysohn Lemma says that there exists a smooth function $f:M\rightarrow [0,1]$ such that $f(C_0)=\{0\},f(C_1)=\{1\}$.
Is it always possible to choose such a smooth Urysohn function such that $0$ is a regular value of $f$ i.e. at each point of $x\in f^{-1}(0)$ the derivative map $df_x:T_x(M)\rightarrow T_0([0,1])=\Bbb R$ is a surjective.