I have been reading through some material on submanifolds and have come across the following exercise which I'm having trouble understanding:
Let $M$ be a $k$-dimensional submanifold of $\mathbb{R}^n$ and let $x\in M$. Let $\gamma:(-\epsilon,\epsilon)\rightarrow\mathbb{R}^n$ be a smooth curve: $\gamma(t)$ is a smooth map. $\gamma'(t)\in \mathbb{R}^n_{\gamma(t)}$ is the tangent vector of $\gamma$ at $t$. Show that the tangent space $M_x$ consists of all tangent vectors at $0$ of curves $\gamma$ such that $\gamma(t)\in M\;\forall t\in (-\epsilon, \epsilon)$ and $\gamma(0)=x$.
I am having trouble understanding what the question is asking and how I would go about approaching it. Any suggestions?