Question

An electronics manufacturer recently created a new version of a popular device. It also created this function to represent the profit, P(x), in tens of thousands of dollars, that the company will earn based on manufacturing x thousand devices: P(x) = -0.16x2 + 21.6x – 400.

Q: The average rate of change of a function over a given interval can be determined by finding the slope of the line that connects the two points on the function representing the endpoints of the interval. Find the average rate of change of the function from part d over the interval [60, 80].?

Answer 1

Since we are given no other function, we have to assume that P(x) is the "function from part d".

The average rate of change of P(x) on the interval [60, 80] is given by
rate of change = (P(80) - P(60))/(80 - 60) = (304 -320)/20 = -0.8

The average rate of change of P(x) over [60, 80] is -0.8.


_____
Units of the rate of change are ($10k)/(1k units) = $10/unit. That is, the profit drops on average $8 per unit on that interval.