A manufacturer estimates the profit on producing x units of its product at...

A manufacturer estimates the profit on producing x units of its product at

a. What is the average rate of change in the profit as the number of units changes from x to x + h?

b. Use the result in part (a) to find the average rate of change in the profit as the number of units produced changes from 25 to 50.

c. What is the instantaneous rate of change in the profit when 25 units are produced?

d. Sketch the graph of y = P(x) and the line that passes through the points (25, P(25)) and (50, P(50)).