Suppose that the marginal revenue for a certain product is given by , where x is in thousand of units and revenue is in thousands of dollars. Find . Round your calculations to two decimal places, if necessary.

Question

Suppose that the marginal revenue for a certain product is given by  , where x is in thousand of units and revenue is in thousands of dollars. Find  . Round your calculations to two decimal places, if necessary. ​

Quizplus · Accepted Answer

To find marginal revenue, we take the derivative of the revenue function with respect to x. Therefore, we integrate the marginal revenue function with respect to x to find the revenue function. Using the power rule of integration, we get:

Revenue = ∫ 11x dx = 11/2 x^2 + C

where C is the constant of integration. Since the revenue is in thousands of dollars, we need to multiply the expression above by 1000. Also, we know that the revenue is equal to $0 when x = 0, so we can use this information to solve for C. Thus, we have:

0 = 11/2 (0)^2 + C
C = 0

Therefore, the revenue function is:

Revenue = 11/2 x^2

To find the marginal revenue function, we take the derivative of the revenue function with respect to x. Thus:

Marginal revenue = d(11/2 x^2)/dx = 11x

Therefore, the answer is E, 11x.

Suppose That the Marginal Revenue for a Certain Product Is