Critical points practice Let's take a look at a specific example. Suppose we are given the function f of (x, y) equals x squared minus 2xy plus 3 y squared plus 2x minus 2y. In order to determine whether it is possible to minimize or maximize this function, we must first find its partial derivatives. Remember that y is a constant. If we differentiate this function with respect to y, we get 0 – 2x + 6y – 2 = 0. We want to solve these two equations simultaneously, so remember that if you have two equations with two unknowns and you're trying to solve them, it's good to try to simplify by adding or subtracting them or whatever. However, you must keep two equations in the end. If you have two equations, you should not expect one of them to disappear. As an example, here, we can simplify things by summing them together. See, if we add them together, the x's cancel and the constants cancel. And, in fact, we're just left with 4y equals 0. That's pretty good but tells us y should be 0. But then we should of course go back to these and see what else we know. Well now it tells us 2x plus 2 equals 0. The equation tells you that the critical point (x, y) is at (–1, 0).