Another part of Maximization Revenue for Pre Calculus...?

Question

For the demand function p=40-(5x^2), when graphing it with the settings (1.62 >= x >= 1.65) and (43.5 >= y >= 43.6), is this setting appropiate to the context of the problem dealing with the maximum point of the revenue function than graphing p=40-(5x^2) with points (0,40) and ((sqrt8),0)? Does it change the price?

I was thinking it is NOT appropiate, but I cannot explain why. If possible if someone can explain to me more easily why the answer is the way it is. Thanks for helping me out, im not sure if im getting this maximization revenue thingy.

Answer 1

That depends on the context of the problem, which you haven't given us. However, this is a much clearer and fuller explanation than the last time you asked this question.

Since p(x) is the demand function, presumably the revenue function is r(x) = x p(x) = 40x - 5x^3, which has a maximum at x = √(8/3) ≈ 1.63. If this is a price in dollars, there's no point trying to get any accuracy beyond the first two decimal places as the unit price will have to wind up being a whole number of cents. In addition, you can obviously only see a small part of the demand curve here, so any larger trends woud be lost. In general you should graph first at a range which allows you to see the overall behaviour of the function, and only zoom in when you need more accuracy for a particular solution.

Answer 2

Not certain what the hint role in your calculator does... from the context of the challenge apparently it does a few form of sensible approximation over the chosen neighborhood. In amy case, in one million) you're watching at very small areas of the graph. This makes the graph appear close to flat, and makes the curvature difficult to decide upon up, so estimating wherein the highest might be is tricky. In two) you're watching at a extra consultant part of the graph, so your outcome usually are extra correct. Of path it is visible from the sort of the role that the highest is at (zero, forty), however under no circumstances brain. ;-)