00:01
In this problem, we have to locate all the critical points of the function f xy equal.
00:07
So this is the function f x, comma y, equal 4x minus x square minus 2xy square.
00:17
So we have to list all the critical points.
00:20
Now the critical points are the points are the values of x and y, where the first order partial derivatives of xy, that is f, x x comma y and f y x x comma y are 0 are minuses so we will find the values where f x comma y equal 0 and fy x comma y equal 0 so here we have given the function f xy so we will find the first order partial derivatives f xx x comma y this is equal to del y del x and function f x y 4x minus x square minus 2x y square so this is equal to 4 minus 2x minus y 2y square we have f x x x comma y equal 4 minus 2x minus 2y square we have f x xxxx minus 2y square now we will find the partial derivatives with respect to y.
01:38
So fy x comma y equal del by del y, f xy that is 4x minus x square minus 2xy square.
01:53
So this is equal to minus 4xy.
01:58
So we have fy x comma y equal minus 4xy.
02:05
Now we will equate this f x x comma y and f y x y x comma y to zero.
02:12
So equating this to zero, we have f x, x, x, x, comma, equals 0 implies 4 minus 2x minus 2y square equal 0...