00:01
All right, we want to determine whether this function has a maximum or a minimum value and then find what it is.
00:08
So there's two ways to do it.
00:11
So let's do it both ways.
00:12
First of all, this is the algebra way.
00:16
This is a parabola and the coefficient of the x squared is negative.
00:21
So it's an upside down parabola.
00:24
So we have a maximum.
00:27
So all we have to do is find the vertex and then we can figure out what the maximum is.
00:32
So what we're going to do is we're going to complete the square, factor out the minus 4 out of the first two, and leave a space where you're going to complete the square.
00:51
All right, so take half of negative 6, which is negative 3, and then square it, which is 9.
00:59
So you've added a 9 in there, but you really didn't add 9.
01:03
You really added negative 4 times 9.
01:05
So you really added negative 36, so you have to have positive 36 over here.
01:12
So you get negative 4 times x minus 3 squared plus 39.
01:18
So we have a maximum at x equals 3 of y equals 39...
