Let:
$$f(x,y)=x^2+2y^2$$
It is required to obtain the maximum value of the above function subject to the constraint $$y-x^2+1=0.$$
I know how to maximize a function of two variables using the usual calculus method of finding the partial derivatives. But given a constraint, i have no idea how to proceed. One thing I tried is to obtain the value of $x^2$ from the constraint and substitute it to the two variable function. In that way, i get a one variable function which is entirely depending on $y$. Then, i tried to differentiate the obtained expression with respect to $y$. This is not giving me the desired result and i am stuck here. Any help would be very beneficial for me. Thanks.
Best Answer
Substituting $x^2$ of your constraint equation:
$f(y)= y+1+ 2y^2.$
This function is not bounded above .