My calculus knowledge is pretty limited, but unfortunately I need to solve a problem of the following kind:
I'm given a 2 dimensional function $f(x,y)$ from $\mathbb{R}^2$ to $\mathbb{R}$ and I want to know, where it attains its minimum value over $\mathbb{R}\times(a,b)$.
Put differently I want to find an $x$ value and a $y\in(a,b)$ such that f(x,y) \leq f(x',y') for all x' in $\mathbb{R}$ and all $y \in (a,b)$.
I'll have to take the partial derivative of $f$ w.r.t $x$, but I don't understand how y will come into play.