What is the range of the derivative of $g(x) = f(x)/(x+1)$, where $f(x)$ is differentiable on $x\in[0,5]$? Let $g(x) = f(x)/(x+1)$, where $f(x)$ is differentiable on $x\in[0,5]$, such that $f(0)=4$ and $f(5)=-1$. What is the range of values $g'(c)$ for a $c$ belonging to $[0,5]$?
Considering values of $f(x_i)$, $f(x)$ must decrease at least once from $0$ to $5$. But that is all the information I can use here. Is there anything I am missing?

This question indeed seems to be incomplete. For instance, if there exists a 
$c\in(0,5)$ such that $$c=\dfrac{-1+2f'(c)\pm\sqrt{4\big(f'(c)\big)^2-8f''(c)f(c)} }{2f''(c)}$$ then $g'(x)$ attains a local maximum on $(0,5)$. To know if this is the case we need way more information on $f$.
If we were given, that $f$ is twice differentiable on $[0,5]$, then we could use the above to conclude at least that the range of $g'$ is bounded. But as I said, this question does not seem solvable, with the information we're given.
