We have a differentiable manifold $X$ embedded in $\mathbb{R}^{n+1}$ and let $h: X \to \mathbb{R}$ as $h(x_{1},...,x_{n+1})=x_{n+1}$. We need to prove that $h$ is a Morse function.
I don't know how to prove this: my idea was to calculate the derivative $dh_{x}$, doing a parametrization $\phi:U \rightarrow X$ of $X$ around x and see what $d(h\circ\phi)_{x}$ and $d \phi^{-1}_{x}$ are.
But I have no idea besides this.
Any help would be really appreciated, thanks!