Sorry for the long title, I wasn't sure how to explain this exactly.
Let's say I have the following function
$f(x,y) = x^2 + 2y$
I want to find the extrema of this function with respect to $x$ and $y$ to try and minimize it. So normally, I would set the partial derivative of the function wrt each variable and set them to zero.
$\frac{\partial f}{\partial x} = 2x$
$2x = 0 \Rightarrow x = 0$
So we can say that $x=0$ minimizes this function.
But what can we say about $y$ exactly?
$\frac{\partial f}{\partial y} = 2$
$2= 0$ is nonsensical
Perhaps these types of optimization problems are somehow degenerate?
$\frac{df}{dy}=2$ just means that the derivative is never $0$, so there are no critical points. You can make the function value as small as you want by making $y$ small, so there is no minimum.