Answer:
The marginal profit function can be found by subtracting the marginal cost from the marginal revenue. The marginal cost is given by the derivative of the cost function, and the marginal revenue is given by the derivative of the revenue function.
The derivative of the cost function is:
C'(x) = dC(x)/dx = 0.9
The derivative of the revenue function is:
C'(x) = dC(x)/dx = 0.9
The derivative of the revenue function is:
R'(x) = dR(x)/dx = 9 - 0.04x
Therefore, the marginal profit function is:
P'(x) = R'(x) - C'(x) = 9 - 0.04x - 0.9 = 8.1 - 0.04x