00:01
For this problem, we are asked to find the points on the ellipse x squared plus 2y squared equals 1, where f of xy equals x times y has its extreme values.
00:09
So we want to take the gradient of f and set that to be equal to lambda times the gradient of our constraint equation g.
00:16
Taking the partial derivative with respect to x gives us that y must be equal to 2 times lambda times x, or that lambda must be equal to y over 2x.
00:27
Then taking the partial with respect to y gives us that x must be equal to 4 times lambda times y, which in turn gives us that lambda must be equal to x over 4 y.
00:42
And we have then that x over 4 y must be equal to y, oops, y over 2x.
00:51
So we have that 2x squared must be equal to 4 times y squared, or that x squared must be equal to 2 y squared, and then that gives us that the absolute value of x must be equal to the square root of 2 times the absolute value of y...