This is a rather simple problem, but i can't for the life of me figure out the logic behind it.
The revenue $R $ from a software product depends on the price $p$ charged by the distributor according to the formula.
$$R = 4000p-10p^2$$
How sensitive is $R$ to $p$ when p is a) $100 $, b)$200$ c)$300 $?
Which begs for the differentiation: $\frac {dR}{dp}=4000-20p$
Now, finding the rate of change is easy. The rate of change is $2000$, $0$, $-2000$ for the respective values $100$, $200$, $300$.
If we were to maximize the revenue we would go for the $200$ option, because it is an absolute maximum value in the function $R = 4000p-10p^2$.
But practically, doesn't it mean that the revenue is $0$ dollars per dollar charged. And that a price at $200$ dollars would give us the revenue of $2000$ dollars per dollar charged?
Plot the revenue curve and see how revenue changes at random $dp$ intervals on the price axis. At the maxima it barely changes with small price shifts, right? Since growth rate of parabola is very small at the start. Now check some remote intervals