If , , , find the extremum of .

I find and and equate them to zero. Then from these two equations, I get .

Can anyone help me to proceed from here to get the extremum?

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- March 17th 2011, 12:40 AMproblemExtremum of f
If , , , find the extremum of .

I find and and equate them to zero. Then from these two equations, I get .

Can anyone help me to proceed from here to get the extremum? - March 17th 2011, 01:11 AMCaptainBlack
- March 17th 2011, 04:18 AMHallsofIvy
Not quite. x, y in and cos(x)= cos(y) implies either x= y or . Put those into the two equations cos(x)+ cos(x+y)= 0 and cos(y)+ cos(x+y)= 0.

(Although I don't believe that second case gives a new solution.) - March 17th 2011, 09:08 AMproblem
By getting or , we still can not imply anything for a critical value as we have and in between and .

Is it that we still have to create another equation to get the critical value?

By the way, the answer given is is the minimum and is the maximum value. - March 17th 2011, 11:16 AMHallsofIvy
If x= y, then sin(x)+ sin(y)+ sin(x+ y)= sin(x)+ sin(x)+ sin(x+x)= 2sin(x)+ sin(2x).

Quote:

By the way, the answer given is is the minimum and is the maximum value.

- March 17th 2011, 08:04 PMCaptainBlack