Question

Use a graph or level curves to find the local maximum and minimum values and saddle points of the function. Then use calculus to find these values precisely. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x,y)=sin(x)+sin(y)+sin(x+y)+4, 0≤x≤2π, 0≤y≤2π
I don't know how to find these values precisely.

Answer 1

You need ∂f/∂x=0 and ∂f/∂y=0
∂f/∂x = cosx+cos(x+y)
∂f/∂y = cosy+cos(x+y)
clearly, this holds at (π,π), which is a saddle point
The max/minima will have to be found using some numeric technique, but I get
max at (1.0472,1.0472)
min at (-1.0472,-1.0472)

Answer 2

okay, why does it says use calculus to find these values precisely? How do I do that?