Business Econ: Limits and Continuity

Question

Suppose that the total profit in hundreds of dollars from selling x items is given by P(x)=5x^2-5x+9.

a.) Find the average rate of change of profit as x changes from 4 to 6.

$_ per item

Answer 1

The rate of change, which you can also think of as the slope of the line connecting the two points of the function at x = 4 and x = 6, can be found using the slope formula (f(6) - f(4))/(6 - 4). f(4) = 69 and f(6) = 159, so the average rate of change between 4 and 6 is (159-69)/(6-4) = 90/2 = 45. And since the unit of f(x) is hundreds of dollars, the rate of change would be $4500 per item.