how is the marginal profit graph related to the profit graph?
I think the marginal profit graph is the derivative of its profit graph.
And so when the marginal profit is the greatest, what does that mean in terms of the original profit equation?
how is the marginal profit graph related to the profit graph?
I think the marginal profit graph is the derivative of its profit graph.
And so when the marginal profit is the greatest, what does that mean in terms of the original profit equation?
If you had a function on integers, f(n)= profit made by selling n items, then the "marginal profit" would be the profit from selling one more: f(n+1)- f(n)= [f(n+1)- f(n)]/1. In the continuous case, f(x)= profit from selling x "gallons" (so it makes sense to have fractional x), the marginal profit is, as you say, the derivative, lim [f(x+h)- f(x)]/h. And the derivative is, of course, the slope of the tangent line to the graph.