calculus
posted by Help Please on .
find max, min and saddle points of the give function f(x,y)=sin(x)+sin(y)+sin(x+y)
0<=x<=pi/4
0<=y<=pi/4
i have that
dz/dx=cos(x)+cos(x+y)
dz/dy=cos(y)+cos(x+y)
and i set them equal to zero but im kinda confused on how to really solve that. i mean i got an answer but that was just from plugging things in and seeing if they worked but i want to know if i can actually solve this without doing that. do i use a trig identity? cause i did that and it came out pretty ugly.

Your going to need fxx, fyy, and fxy too. For your critical values of the dz's, you will need to change the cos(x+y) to their proper trig identity because you cant solve for the CV with what you have
d=fxx*fyyfxy^2
if d=0, then its a saddle point
if d>0 and so is fxx, then it is a min value
if D>0, but fxx is <0, then its a max value