Critical points points where the derivative is zero or not de ned. Second derivative test for functions with one variable. There is a test that can tell us local max or local min. Second derivative test for functions with two variables. We know that f = f = 0 at the critical point. Saddle point: x - y critical point at (0,0) Saddle point: x + y critical point at (0,0) Saddle point if a and c are different signs. Now say that b 0, try completing the square. Maximum if a is negative and ac-b is postive. Now f(x,y) f = f = 0, a = f , b=f , c=f. Example: 13. 10 #5 f = 2x + 2xy + y + 4x - 2y +1 f = 4x + 2y + 4 and f = 2x + 2y - 2 with a critical point at (-3,4)