00:01
Okay, 6 .2 number 36.
00:02
Look at the question.
00:03
We're given this function for p, which is the percent of a population affected by a disease after t days.
00:10
We're asked to maximize this, and we do, we want to maximize.
00:16
We need to check the critical numbers or critical points, and we need to check the end points, and we are given the end points zero to 40.
00:28
First thing we need to do is check these critical numbers, so we need to check the end points.
00:31
So we need to check the end points.
00:31
Start by finding the derivative.
00:33
This is going to be a product rule.
00:35
We have 10t, which is the first, and we have e to the negative t over 8, which is going to be our second product.
00:44
So to find p prime of t, we're going to have the first, which is 10t, times the derivative of the second, which is negative 1 over 8, e to the negative t over 8, plus the 7.
01:02
Second equation, just copied down, times the derivative of the first, which is 10.
01:10
Some simplification and writing, we can factor some stuff out.
01:15
We can factor out a 10 to the negative t over 8.
01:22
If we factor that out from here, we're just left with negative 1 over 8t plus 1...