00:01
Alright, so here we have to have two numbers that add to negative 18 and we want to find the maximum product that we can have.
00:08
So if we think of the two numbers x plus y, those are the two numbers, it's going to add up to negative 18.
00:19
That's the sum.
00:21
Now we want to find the max product.
00:23
So the product is going to equal xy.
00:27
Well that has x's and y's in it.
00:29
I just want it with x.
00:30
So if i solve this for y, y equals negative x minus 18, i can substitute this in for y and now i have my product function with just x as the variable and it's going to be x times negative x minus 18.
00:51
Okay, if i want to maximize that i just have to take the derivative.
00:56
So let me clean this up to make the derivative easier.
00:59
So p prime of x is going to be negative 2x minus 18.
01:08
We're going to set that equal to zero.
01:12
So when i add the 2x i get negative 18 equals 2x.
01:16
Divide by 2, x is going to equal negative 9...