Assignment 2: Critical (Stationary) Points of a Bivariate Function flx,y). Let us recall first the case of a function of one variable f(x). Points xc where df/dx-0 are called critical points (also known as stationary points). At critical points, the tangent line is horizontal. The second derivative test is employed to determine if a critical point is a local maximum or a local minimum: If dif/dx"(%) > 0, then Xc is a local minimum. If d2f/dx"(x) 0 and f/dx2 0 and 02f/d2 >0, then f(x,y) has a relative minimum at (Xc , yc). Assignment 2: Critical (Stationary) Points of a Bivariate Function flx,y). Let us recall first the case of a function of one variable f(x). Points xc where df/dx-0 are called critical points (also known as stationary points). At critical points, the tangent line is horizontal. The second derivative test is employed to determine if a critical point is a local maximum or a local minimum: If dif/dx"(%) > 0, then Xc is a local minimum. If d2f/dx"(x) 0 and f/dx2 0 and 02f/d2 >0, then f(x,y) has a relative minimum at (Xc , yc)