Suppose that the total profit in hundreds of dollars from selling x items is given by
P(x) = 5x^2 - 7x + 8.
Complete parts a through d below.

a. Find the average rate of change of profit as x changes from 4 to 6.
b. Find the average rate of change of profit as x changes from 4 to 5.
c. Find and interpret the instantaneous rate of change of profit with respect to the number of items produced when x = 4. (This number is called the marginal profit at x = 4.)

What does this result mean? Choose the correct answer below.

a. when 4 items are sold, the profit is decreasing at the rate of $ per item.
b. When 4 items are sold, the profit is increasing at the rate of $ per item.
c. When items are sold for $ the profit is increasing at the rate of $4 per item.
d. When items are sold for $ the profit is decreasing at the rate of $4 per item.

d. Find the marginal profit at x = 6.