Find the critical point(s) of f(x, y)=sinx+siny+cos(x+y) for 0≤x≤pi/4 and 0≤y≤pi/4. classify each as local max, min or saddle point?
I know the min is 1, but how do you find the max?
It is pretty easy to show that there is NO point in the interior of and where grad f is 0 so any max and min must on the boundary. One boundary is the line x= 0: on that line f(0, y)= sin(y)+ cos(y). Is there any place on that line where f_y(0, y)= 0. Another is the line : on that line . Is there any place on that line where ? Of course the same thing applies to the lines and . Any you need to check the values at the corners: , , , .