00:01
In this question, we are asked to find the maximum and the minimum values of the function f subject to the given constraint.
00:07
To do that, we need to solve the system of equations.
00:10
The gradient of f equals to lambda multiplied by the gradient of g, and x squared plus y squared equals to 5.
00:23
Where g is basically the left -hand side of the constraint equation.
00:30
So it's x squared plus y squared, minus 5.
00:34
All right, now let's calculate the gradient of the function f.
00:40
The gradient of f equals to the vector with the coordinates fx and fy.
00:49
In our case, the derivative of f with respect to x equals to 2, and the derivative of f with respect to y equals to 4.
00:58
The gradient of g equals to g x and gy, and the derivative of g with respect to x equals to 2x, the derivative of g with respect to x equals to 2y.
01:17
Therefore, we can write the system of equations as 2 -4 equals to lambda multiplied by 2x and 2y.
01:32
And we'll just rewrite the second equation, x squared plus y squared equals to 5.
01:41
We can write the first vector equation as 2 scalar equations, 2 -lambda x, and 4 equals to 2 lambda y...