1. The problem statement, all variables and given/known data Find the critical points of the function f(x, y) = sinx + siny + cos(x+y) where 0<=x<=pi/4 and 0<=y<=pi/4 2. Relevant equations First and second order partial derivative of f(x, y) 3. The attempt at a solution To find the critical points, I first find the first partial derivative with respect to x and y. fx(x,y) = cosx - sin(x+y) fy(x,y) = cosy - sin(x+y) Set both of the first partial derivative = 0 cosx = sin(x+y) x=pi/4 and y=0 cosy = sin(x+y) x=0 and y=pi/4 Here is where I got stuck, I noticed two points where the above equations are true, but how do I find all the critical points? I checked the two points I found using D = fxxfyy - (fxy)^2 fxx = -sinx - cos(x+y) fyy = -siny - cos(x+y) fxy = -cos(x+y) and I found that D for both points are less than zero, which suggest that they both are saddle points. I then graphed the function f(x, y) and these two points don't appear to be saddle points on f. I assume that I made some mistake somewhere either in the derivative or the graph, if someone can check this for me, it would be greatly appreciated.