Find the absolute (global) extrema

[A.k]

Given real function of two variables: f(x, y) = sin x + sin y + sin(x + y)
and set G = {[x; y] ∈ E2 : x ∈ <0; π 2 >, y ∈ <0; π 2 >}.
Find the absolute (global) extrema of the given function f on the set G.
Hint: You may need the formula cos α + cos β = 2( (cos α+β /2 )*(cos α−β)/ 2)

 

[Deleted member 4993]

Given real function of two variables: f(x, y) = sin x + sin y + sin(x + y)
and set G = {[x; y] ∈ E2 : x ∈ <0; π 2 >, y ∈ <0; π 2 >}.
Find the absolute (global) extrema of the given function f on the set G.
Hint: You may need the formula cos α + cos β = 2( (cos α+β /2 )*(cos α−β)/ 2)

What are the characteristics of global maxima/minima?

How is it different from local maxima/minima?

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Dr.Peterson]

Given real function of two variables: f(x, y) = sin x + sin y + sin(x + y)
and set G = {[x; y] ∈ E2 : x ∈ <0; π 2 >, y ∈ <0; π 2 >}.
Find the absolute (global) extrema of the given function f on the set G.
Hint: You may need the formula cos α + cos β = 2( (cos α+β /2 )*(cos α−β)/ 2)

Please explain the notation in "G = {[x; y] ∈ E2 : x ∈ <0; π 2 >, y ∈ <0; π 2 >}"; I can guess parts of it, but I don't know E2.

What derivatives have you found? Where do you need help?

Also, please be careful to use parentheses where needed. I think you meant cos α + cos β = 2( (cos ((α+β)/2) )*(cos ((α−β)/ 2)).