Question

Explain why the following is false:
If (a,b) gives rise to a (constrained) relative extrema of f subject to the constraint g(x,y)=0, then (a,b) also gives rise to the unconstrained relative extrema of f. Explain why the following is false:
If (a,b) gives rise to a (constrained) relative extrema of f subject to the constraint g(x,y)=0, then (a,b) also gives rise to the unconstrained relative extrema of f. @Mathematics

Answer 1

we are studying Lagrange Multipliers if that helps :)

Answer 2

easy to see by an example

if \[f(x,y)=x^2+y^2\] then is is clear that f(x,y) has no max
but if we constrain on the plane x+y+z-1=0 it is easy to see that there is an absolute max