let $f(x,y) = 2\pi x(x+y)$ be the function for a cylinder area with x as radius and y as height
let $g(x,y) = \pi x^2 y = 1$ be the constraint (Volume)
I solved this by finding the stationary point/points to the Lagrange function $L(x,y,\lambda)$ (At least thats what i think the definition is) which is guaranteed to be minima or maxima to $f(x,y)$ given constraints $g(x,y)=C$.
The problem im having is that i got the maxima of $f(x,y)$ at the point $(\sqrt[3]{1/2\pi},2\sqrt[3]{1/2\pi})$ and as the question states im interested in the minima. Im kind of lost as what i should do right now.