f(x,y)=sinx+siny+sin(x+y), 0<=x<=2π 0<=y<=2π

Question

Find the extrema of f and state their nature

show solution step

Answer 1

for extrema, you need ∂f/∂x and ∂f/∂y = 0

∂f/∂x = cosx + cos(x+y) = 0
∂f/∂y = cosy + cos(x+y) = 0

recall that

cos π/3 = -cos(2π/3)

So that should get you started.