Final answer:
To answer these questions, we need to understand the concepts of total cost, total revenue, and profit. We can find the value of x where the graph of R(x) has a horizontal tangent line by finding the critical points of R(x) and setting the derivative equal to zero. The profit function P(x) can be found by subtracting the total cost from the total revenue.
Step-by-step explanation:
To answer these questions, we need to understand the concepts of total cost, total revenue, and profit.
(A) To find the value of x where the graph of R(x) has a horizontal tangent line, we need to find the critical points of R(x). We can do this by finding the derivative of R(x) with respect to x and setting it equal to zero. The critical points will be the values of x where the derivative is zero.
(B) The profit function P(x) can be found by subtracting the total cost from the total revenue: P(x) = R(x) - C(x).
(C) To find the value of x where the graph of P(x) has a horizontal tangent line, we need to find the critical points of P(x). We can do this by finding the derivative of P(x) with respect to x and setting it equal to zero.
(D) To graph C(x), R(x), and P(x) on the same coordinate system, we can plot points for different values of x in the given range, and then connect the points to form the graphs. The break-even points can be found by finding the x-intercepts of the graph of P(x), which are the values of x where the profit is zero.