Question

The Demand function for a product is given by:

D(q) = - 0.0003q^2 - 0.04q + 23.56

where q is the number of units sold and D(q) is the corresponding price per unit, in dollars. What is the average rate of change of Demand between 40 and 175 units sold?

Answer 1

The average rate of change of Demand between 40 and 175 units sold is of -0.1045.

Explanation:

Average rate of change:

The average rate of a function f(x) in an interval [a,b] is given by:

`A = (f(b) - f(a))/(b - a)`

In this question:

`D(q) = -0.0003q^2 - 0.04q + 23.56`

What is the average rate of change of Demand between 40 and 175 units sold?

`a = 40, b = 175`. So

`D(40) = -0.0003*40^2 - 0.04*40 + 23.56 = 21.48`

`D(175) = -0.0003*175^2 - 0.04*175 + 23.56 = 7.3725`

So

`A = (f(b) - f(a))/(b - a) = (7.3725 - 21.48)/(175 - 40) = -0.1045`

The average rate of change of Demand between 40 and 175 units sold is of -0.1045.