Find the marginal cost, marginal revenue, and marginal profit functions. find all values of x for which the marginal profit is zero.

c(x) = 5x
r(x) = 8x − 0.001x^2

Let P(x) be the profit function and is equivalent to the difference of revenue and cost.
P(x) = R(x) - C(x)
P(x) = 8x - 0.001x² - 5x
P(x) = 3x - 0.001x² 
Profit is 0 so:
0 = 3x - 0.001x²
x = 0, x = 3000
The profit is 0 when x is 0 or 3000.