Explain why the following is true of false:
If (a,b) gives rise to a (constrained) relative extremum of f subject to the constraint g(x,y)=0 then fₓ (a,b)=0 and f sub-y(a,b)=0, simultaneously. Explain why the following is true of false:
If (a,b) gives rise to a (constrained) relative extremum of f subject to the constraint g(x,y)=0 then fₓ (a,b)=0 and f sub-y(a,b)=0, simultaneously. @Mathematics

Question

Explain why the following is true of false:
If (a,b) gives rise to a (constrained) relative extremum of f subject to the constraint g(x,y)=0 then fₓ (a,b)=0 and f sub-y(a,b)=0, simultaneously.  Explain why the following is true of false:
If (a,b) gives rise to a (constrained) relative extremum of f subject to the constraint g(x,y)=0 then fₓ (a,b)=0 and f sub-y(a,b)=0, simultaneously.  @Mathematics