I'm currently sturrling with the Lagrange-Multiplier. I do get it in theory but I kind of fail knowing when to use it.
Usually I get exercises like this:
Let $f:\mathbb R^n \to \mathbb R^m$ be some function and let A be some set.
I know, if I can parametrize A so that I get a function $g=0$ representing it's surface, can use lagrangian - right?
But what if I have $f: A \to R^m$ whereas $A\subset \mathbb R^n$, can I still use it or not?
Example: $A=\{(x,y,z)\in \mathbb R^3 | x^2+2y^2+3z^2 \leq 1\}$
$f: A\to\mathbb R, \quad (x,y,z)\mapsto x^2-y^2+1$
If I can find a parametrization for $A$ I could use Lagrange-Multipliers here, right? (for local points only)