Multivariable Calc Confusion...

In the definition of Lagrange multipliers, we define a function f of n non-independent variables and a function of g that is a constraint of f (related to f somehow?).

This relationship is confusing to me, can someone explain the relationship between these two functions using a simple example? How do you think about these two equations?

Question

Multivariable Calc Confusion...

In the definition of Lagrange multipliers, we define a function f of n non-independent variables and a function of g that is a constraint of f (related to f somehow?).

This relationship is confusing to me, can someone explain the relationship between these two functions using a simple example? How do you think about these two equations?

anonymous · Answer

g(x,y) allows you to use a constraint so you can hone in on a subset of the minima