Calculate the maximum loss, given the marginal revenue function R'(x) = x2 and marginal cost function C'(x) = 4 - 3x. (Hint: Integrate the marginal profit function over the region where C'(x) > R'(x) for x>0.

First, it's a bit hard to understand the question since the formulas don't appear proprly. I will assume that what you have is this:


C(x) = 4 - 3x \\
R(x) = x^2


where C(x) is the marginal cost function and R(x) is the marginal revenue function. Please confirm.

The marginal loss is the difference between the marginal cost and the marginal revenue:


L(x) = C(x)-R(x)
.

The total loss at any point A is the integral of this:


Loss (A) = \displaystyle \int_0 ^A L(x) dx = \displaystyle \int_0 ^A (4-3x - x^2) dx


So, to find the point A that gives the maximum loss you need to first solve for C(x) = R(x). Then perform this integral to find the amount of the loss at that point.