1. Suppose that the quantity x is 1000's, and price p in dollars are related by the price demand equation x2 + 5px + 10p = 220 dx a) Use implicit differentiation to find an equation involving dp - and at - b) If the price of the commodity is decreasing at a rate of $1 per month when the price is $2 and demand is 10. Find the rate of change of demand.2' Assume the demand for a product is given by q = f (p) = 150 p a) Find the elasticity function in terms of p. b) Find the elasticity when the price is $50. c) For which price values, does a decrease in price increase revenue? 3. A pulley is on the edge of dock 8 feet above the water. A rope is being used to pull in a boat. The rope is attached to the boat at water level. Boat x a) Let r = the distance from dock of the boat and T = the length of the rope Write an equation relating x and r, b) Diercntiatc the equation implicitly with respect to time, t. e) If the rope is being pulled in at a rate of 1 foot per second. At What velocity is the boat approaching the dock at the instant boat is 6 feet from the dock