I came across this exercise in Warner's Foundations of Differential Manifolds and Lie Groups,
Let $N \subset M$ be a submanifold. Let $\gamma \colon (a,b) \to M$ be a $C^{\infty}$ curve such that $\gamma(a,b) \subset N$. Show that it is not necessarily true that $\dot \gamma (t) \in T_{\gamma(t)}N$ for each $t \in (a,b)$.
I'm having trouble trying to find an example of such a curve. Could someone give me an example or show me the way? Either way thanks!