00:01
Here's our function for profit, and the rate of change of profit is the derivative of p with respect to q.
00:13
So that's p prime as a function of q.
00:17
Okay, so we take the derivative with respect to q.
00:20
We're going to use the product rule.
00:22
So first i will take the derivative of this factor while holding the second factor constant.
00:30
So that's 77 times e to the negative 0 .2q.
00:39
And now i'm going to add the next term, which involves holding this first factor constant while taking the derivative of the second one.
00:48
So i have 77q times negative 0 .2 times e to the negative 0 .2 times e to the negative 0 .2 q.
01:01
And i can take out a factor of 77e to the negative 0 .2q.
01:10
So i have 1 minus 0 .2q.
01:18
Okay, so this is our rate of change of profit.
01:26
Now we need to find the production level q such that the rate of change of profit is zero.
01:33
So let's set p prime equal to zero...