# Lagrange Multipliers.

1. May 24, 2008

### MathematicalPhysicist

I need to prove with the help of LM, that for a^2+b^2+c^2=1 we've got: |a^3b^2c|<0.05.

Now I used Lagrange multipliers on the function: f(a,b,c)=a^3b^2c, one thing that lagrange multipliers can assure me is that the points i find are extremum, now i find points which give me that f=0 which are ofcourse in absolute value are the minimum points, and i also found points where i get that |f(a,b,c)|<=0.48... something like this, but how do i know that this is an absolute maximum, obviously i need to check on the boundary which is the sphere, on the interior it's obviously a maxima, but how to show that it's absolute maximal?