Question

find the absolute maximum and minimum for the function f(x)=x+yz on the ball B = {(x, y, z) | x^2 + y^2 + z^2 =< 1}.

Answer 1

find all your critical points ....throw out any not in your ball...then use Lagrange multipliers to check the boundary condition

Answer 2

I found that x=1, and y=z
which imply that critical point is (1,0,0)
how to find the minimum

Answer 3

why is that the only critical point?

Also you need to check the entire boundary

Answer 4

How to find other critical point?

Answer 5

f(x)=x+yz ??

or

f(x,y,z)=x+yz ??

Answer 6

yes, you are right
f(x,y,z)=x+yz
subject to x^2+y^2+z^2<=1
find maximium and minimum
I use Lagrange multipliers and found that x=1 and y^2=z^2
by plug in into constraint, I found critical point (1,0,0)
how to find other critical points?