Question

help on multivariable calc T-T... what are the relative extrema of f(x,y) = x^2 + e^y? is the answer none...?

Answer 1

clearly domain is \(\mathbb{R}^2\) and for relative extrema we have\[\frac{\partial f}{\partial x}=2x=0\]\[\frac{\partial f}{\partial y}=e^y=0\]we should solve these equations simultaneously but u r right...answer is none because for all real values of y we have\[e^y>0\]