00:01
In this question, whereas to find the maximum values of the function x, y squared, subject to the constraint x squared plus y squared equals to 3.
00:09
To do that, we'll use the lagrange multipliers method, and first we need to define the function g, by moving everything in the constraint equation to the left hand side.
00:23
So, g will be equal to x squared plus y squared minus 3.
00:27
Next, we need to solve the system of equations, the gradient of f equals to lambda times the gradient of g.
00:34
And x squared plus y squared equals to 3.
00:41
The gradient of f equals to y squared and 2xy, and the gradient of g equals to 2x to y.
00:55
Therefore, the system of equations becomes at y squared 2xy equals to lambda times 2x to y and x squared plus y squared equals to 3.
01:17
We can rewrite this coordinate twice as x is y squared equal to x.
01:20
To 2 lambda x and 2xy equals to 2y and x squared plus y squared equals to 3.
01:35
From the second equation we are going to get that 2y times x minus 1 equals 0.
01:48
The first and the third equations are going to be same.
01:57
Now the second equation gives us two possibilities.
02:03
Either y equals 0, or x equals 1.
02:10
If y equals 0, we are going to get that 0 equals to 2 lambda x and x squared equals to 3.
02:24
And this would imply that x must be equal to plus minus square root of 3 and y must be equal to 0.
02:33
Now if x equals to 1, we are going to get that y squared equals to 2 lambda...