. Rearrange this result to match the point-slope form you constructed above. General rate of change Now suppose that we have a more general function for our marginal profit, MP(q), and we still have that profit is $30000 when q = 1000. We can represent the Profit function as follows: P(q) = 30000 + MP(u) du . What are the appropriate limits in the integral above? How do you know? (remember that the overall result of the right hand side is a function, not a number) . Explain the meaning of the right hand side and how it generalizes the idea of point-slope form. o What is the meaning of 30000? o What are the units of the quantity MP(u) * du? What does the integral part describe?1. Leaking Tank A tank of water has a hole and leaks at a rate of L(t) gallons per minute, where t measures time in minutes after you unplug the hole. How can we interpret the meaning of following integrals? Explain your reasoning. L(1) di L(t) dt L(t) dt The integrals above give answers that are numbers. The integral below results in a function. L(u) du What is the independent variable of that function? What is the meaning of the variable u? What are its units? . . . . What is the meaning of the quantity L(u) * du? What is the interpretation of the resulting function?2. Marginal Profit Marginal profit is a measure of the change in total profit as a function of quantity demanded/sold. (Technically, quantity demanded/sold is a discrete amount, but it is common to treat it as a continuous variable to make calculus possible.) Constant Rate of Change Suppose that a particular company is currently producing q = 1000 units and is making a total profit of $30,000. Further, they know that for values between q=800 and q=1200, their marginal profit is constant, at $5 / unit. We will write a description of their profit function in two ways. Algebraic approach Since the rate of change of profit is constant, we know that the profit will follow a linear function. Recall that a linear equation can be written in point-slope form: y -y1 = m(x - x1) or, more appropriately for what I'd like us to see: y = y1+ m(x-x1) . Using the information above, write an equation in point- slope form describing the profit function P(q). (Note, this function is only valid when quantity is between 800 and 1200). Calculus approach . Now, integrate the marginal profit function (here, it is just a constant function). You will get a constant of integration, and you can use the known information (profit = $30000 when q = 1000 units) to solve for that constant of integration. . Rearrange this result to match the point-slope form you constructed above.Highway Driving ::Interstate-95:: runs up and down the East coast of the US. In Florida, 195 starts in Miami and goes 380 miles to Jacksonville. Let H(s) represent the time traveled measured in hours past noon as a function of distance traveled from Miami measured along 195. We can write H(s) = 4+ g(u)du 205 where 0