Show that if $f:M\to \mathbb{R}$ is a positive and proper function and $X$ is a vector field such that $\langle df,X\rangle $ is bounded, then $X$ is complete.
I know that if $X$ is a vector field with compact support, then it is complete, but i do not know how to use the fact that $\langle df,X\rangle $ is bounded.
Thank you!