F(x, y)=eâ8xâx2+8yây2. find and classify all critical points of the function. if there are more blanks than critical points, leave the remaining entries blank.

Presumably, the function is



We have




Both partial derivatives vanish when




so there is only one critical point . The Hessian matrix for is



At the critical point, we have




which indicates that a relative maximum occurs at , and the function takes on a maximum value of .