confusing lagrange multiplier question
subject to x^2+y^2+z^2=1
Find all the absolute maximum and minimum.
I tried to solve the simutaneous equations, and I ended up with 14 critical points! (Headbang)
So I doubt if I did right or wrong.
Can anybody please help me and see how many of them? What are they? I solved that x=o, plus or minus square root 2 on 2, plus or minus 2/3
y=0, plus or minus square root 2 on 2, plus or minus 2/3
z=0, plus or minus 1, plus or minus 1/3
Which rearrange them, I end up with 14 critical points. Am I right? Thanks a lot.