The question I am trying to solve is

$$\begin{array}{ll} \text{extremize} & f(x,y) := xy − 6y − 36x + 216\\ \text{subject to} & y \geq x^2\\ & y \leq 37\end{array}$$

Now I know how to solve these types of questions when the constraints are inequalities on $x$ and $y$, such as $0 \leq x \leq 5$ and $2 \leq y \leq 6$. First, we find the interior critical points and then we find the boundary critical points. Similarly, first, I calculated interior CP and I only got $f(6,36)=0$. Then, I took $x= -\sqrt{37}$ into $f(x,y)$ and got a function of $y$. Then I put in $y=37$ to find the minimum value. It turned out to be correct. The minimum value is 
$f(-\sqrt{37}, 37) = -12.08$. 

But when I take $x=\sqrt{37}$ and $y=37$, value of $f(x,y)$ is $0.08$ and it turns out to be incorrect. I do not know what I am doing wrong and what other values of $x$ or $y$ to take to get another critical point of $f(x,y)$.