00:01
Hi, from the question given that, consider the given function f of x, y is equal to x, y on the ellipse 9x squared plus y squared is equal to 4.
00:15
So here we need to find a minimum and maximum value of f.
00:20
So by using the micron g multiplier, del f is equal to lambda del g.
00:27
So g of x, y is equal to 9x squared plus y squared minus 4.
00:37
So for simplifying this for del f, we obtain y, which is equal to lambda times of 18x.
00:49
And similarly, x is equal to 2y lambda.
00:55
So from this, lambda is equal to x by 2y.
01:00
So y is equal to x by 2y times of 18x.
01:06
So this 2 and 18 will get cancelled, we have 9.
01:10
So this implies y squared is equal to 9x squared.
01:15
Now substitute in the given g of x, y.
01:19
So we have 9x squared or y squared 9x squared minus 4 is equal to 0.
01:29
So this is nothing but 18x squared is equal to 4...