# Multivariable Calc Absolute Extrema Problem

1. Mar 29, 2010

### joemabloe

1. The problem statement, all variables and given/known data
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)

2. Relevant equations

3. 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.

2. Mar 29, 2010

### 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 $\frac{\partial}{\partial y}$.

3. Mar 29, 2010

### joemabloe

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