You are given a function $f(x)$ that is continuous on the closed interval $[-1,4]$ and differentiable on the open interval $(-1,4)$.

If $f(4)=10$ and the average rate of change is bounded between $-4$ and $3$, that is: $-4\le f'(x)\le 3$, what is the smallest possible value for $f(-1)$?