• Support PF! Buy your school textbooks, materials and every day products Here!

Multivariable Calc Absolute Extrema Problem

  • Thread starter joemabloe
  • Start date
  • #1
8
0

Homework Statement


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

Answers and Replies

  • #2
227
0
Do you know [itex]\frac{\partial}{\partial x}\sin(x)[/itex], [itex]\frac{\partial}{\partial x}\sin(y)[/itex] and [itex]\frac{\partial}{\partial x}\sin(x+y)[/itex]? You can use the product rule to put them together- it works the same with partial derivatives. Then do the same but with [itex]\frac{\partial}{\partial y}[/itex].
 
  • #3
8
0
Do you know [itex]\frac{\partial}{\partial x}\sin(x)[/itex], [itex]\frac{\partial}{\partial x}\sin(y)[/itex] and [itex]\frac{\partial}{\partial x}\sin(x+y)[/itex]? You can use the product rule to put them together- it works the same with partial derivatives. Then do the same but with [itex]\frac{\partial}{\partial y}[/itex].

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
 

Related Threads on Multivariable Calc Absolute Extrema Problem

  • Last Post
Replies
16
Views
3K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
907
Top