A company is selling a product at market price that has a daily cost function C(x) = x² + 500 in dollars and a daily revenue function R(x) = 55x in dollars, where x is units sold. 

(a) Determine the coordinates of the break-even points to the nearest hundredth. 

(b) Graph the cost and revenue functions in the window [0, 50, 10] by [0, 3000, 500]. 

(c) Shade the region of the graph that represents profit for the company. 

(d) Use the cost and revenue functions to write the profit function P(x). 

(e) How many units should be sold daily to maximize profit? What is the maximum profit possible?