6. (10 points) Suppose that the total revenue and total cost (in thousands of dollars) from the production and sale of x-hundred stainless steel water bottles are given by R(x) = 2x2 + 12x and C(x) = 23 - x2 + 3x. Find the number of bottles which should be produced and sold to maximize the total profit P(x). You must justify your answer using Calculus strategies discussed in class. (Hint: First find your total profit function P(x) and proceed to maximize it from there. Remember that the domain for P(x) is x 2 0 since the number of bottles should be non-negative)