INSTRUCTOR: Find the critical point of the function f of x comma y equal to x cubed plus 2xy minus 2x minus 4y. A critical point is defined as a point where fx, or f sub x, equals f sub y, equals 0 or where f sub x and f sub y are undefined. So let's begin by finding fx. That is equal to 3x squared plus 2y minus 2. And then f sub y is equal to 2x minus 4.

Now finding where one of these is equal to 0 is often easier with one of the two. So f sub y is equal to 0 clearly whenever x equals 2. So our critical point has an x value of 2. Now, if you evaluate x equals 2 into f sub x, then we see that fx is equal to 2y plus 10, which is equal to 0 whenever y equals negative 5. So our critical point is the point 2 negative 5.