Let $\mathbf c(t)$ be a flow line of a gradient field $\mathbf F = - \nabla V$. Prove that $V(\mathbf c(t))$ is a decreasing function of t.
Not sure where to begin here, although it might have to do with the gradient chain rule?
$$\mathbf c'(t) = \mathbf F(\mathbf c(t)) = -\nabla V(\mathbf c(t))$$
So for $\mathbf c'(t) > 0, \nabla V(\mathbf c(t)) < 0$ indicating that $V$ is decreasing. Is that right?