Answer:
A. Average rate of change = -30
B. x ≥ 0
Explanation:
Part B.
The average rate of change from x = a to x = b can be calculated as
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
In this case, we want to calculate the average rate of change from x = 3 to x = 5, so f(3) = 120 and f(5) = 60. Then
[tex]\frac{f(5)-f(3)}{5-3}=\frac{60-120}{2}=-\frac{60}{2}=-30[/tex]
So, the average rate of change is -30. So, from x = 3 to x = 5, when we increase the price by $1, the profit decreases by $30.
Part C.
The domain is the set of values that the variable x can take. In this case, x is the price of the pens, so it has to be greater than or equal to 0.
Therefore, the constraints for the domain are
x ≥ 0
