Problem:

Find max and/or min values of function f given the contraints:

f(x,y,z) = x^2 +y^2 +z^2

x + y + z = 1

x + 2y + 3z = 6

I know how to use legrange generally. When I solve using both constraints, I get values for x,y,z that when plugged into the function f gives 25/3.

The answer in the book gives: "No Maximum, minimum: 25/3"

My question is how do I know the value i got (25/3) is the minimum and how do I know there is no maximum for the function?