Multivariable Calc Absolute Extrema Problem

[joemabloe]

Homework Statement

F(x,y)= sin(x)sin(y)sin(x+y) over the square 0\underline{}<x\underline{}<pi and 0\underline{}<y\underline{}<pi


(The values for x and y should be from 0 to pi INCLUSIVE)

Homework Equations

The Attempt at a Solution

I know I need to do the partial derivatives in terms of x and y and set them equal to 0 to find the critical points, but I am having some trouble with that.

 

[Tomsk]

Do you know \frac{\partial}{\partial x}\sin(x), \frac{\partial}{\partial x}\sin(y) and \frac{\partial}{\partial x}\sin(x+y)? You can use the product rule to put them together- it works the same with partial derivatives. Then do the same but with \frac{\partial}{\partial y}.

 

[joemabloe]

Do you know \frac{\partial}{\partial x}\sin(x), \frac{\partial}{\partial x}\sin(y) and \frac{\partial}{\partial x}\sin(x+y)? You can use the product rule to put them together- it works the same with partial derivatives. Then do the same but with \frac{\partial}{\partial y}.

I already found that:

partial derivative in terms of x = siny[cosxsin(x+y)+sinxcos(x+y)]
you get y=0, pi because siny =0, but I don't know how to solve for the other solutions


partial derivative in terms of y = sinx[cosysin(x+y)+ sinycos(x+y)]
and you get x=0, pi because sinx=0

and then I have the same problem again and am stuck