The price-demand function and the cost function for the production of HDTVs are as follows: x=9,00030pandC(x)=150,000+30x where x is the number of HDTVs that can be sold at a price of $p per TV and C(x) is the total cost (in dollars) of producing HDTVs. A. Express the price p as a function of the demand x, and find the domain of this function. B. Find the revenue function in terms of x, i.e., R(x), and then state its domain. C. Find the marginal revenue function. D. Find R(3000) and R(6000) and then interpret these quantities. E. Graph the cost function and the revenue function on the same coordinate system for 0x9000. Find the break-even points and indicate regions of loss and profit. F. Find the profit function in terms of x, i.e. (x). G. Find the marginal profit function. H. Find the (1500) and (4500) and then interpret these quantities. The spread of a virus is modeled by V(t)=t2+6t4 where V(t) is the number of people (in hundreds) with the virus and t is the number of weeks since the first case was observed. A. Graph V(t). You must show the coordinate(s) which intersects with the horizontal and vertical axes for full credits. B. What is a reasonable domain of t for this model? Explain why. C. When does the number of cases reach a maximum? What is the maximum number of cases? D. Find the rate of change function. E. What is the rate of change in the number of cases at the maximum? F. Graph the sign (+ or ) of the rate of change up to the maximum and after the maximum. The historical and projected profit (in billions) for Chevron Corp. for the years 2019 through 2026 can be approximated by the following function: (x)=2.3x2+55.2x252.6 where x=9 corresponds to the year 2019 . A. What is the marginal profit for the company in 2024? Interpret the result in your words. B. Derive the vertex form of the profit function and draw the graph. C. Using the concept of derivatives, answer the following questions: (i) when does the local maximum profit occur? and (ii) does it correspond to the graph in part B? Explain. D. What was the maximum profit