The fuel economy is given by kilometers travelled per liter of fuel, so it is given by $y$. Since you are looking for maximum economy, $y$ needs to be maximized. Now, note that $y$ is a function of $S$, so maximizing $y$ means finding a value $S_\max$ of $S$ such that $y(S_\max)$ (written as a function) becomes maximal.
Now, as you mention derivatives, you should know that if $y(S^*)$ is a maximum or minimum, $\frac{dy}{dS}(S^*) = 0$. So, you can find candidate values for $S_\max$ by finding the zeroes of the derivative. Of course, you will then need to show that this is actually a maximum, but this isn't hard...