Answer: -$480
Step-by-step explanation:
The revenue us P*x
now, when P = $40, we have:
X = 14400 - 3*40^2 = 9600
then the revenue is:
9600*$40 = $384000
now, the price increaces by $2 so the new equation is:
X = 14400 - 3*42^2 = 9108
The revenue is:
9109*$42 = $382536
You can see that the revenua is smaller than before.
Now, if we want to calculate the rate of change when p = $40, we need to look at X'(40)
this is:
X´(p) = -3*2*p
then:
X'(40) = -3*2*40 = -120
Theh rate of change of the revenua will be:
X'(40)*$40 = -120*$40 = -$480
