Find the dimensions of the closed right circular cylindrical can of smallest surface area whose volume is $\displaystyle 16pi\;cm^3$.

I managed to find r = 2cm, h = 4cm which gives the surface area of $\displaystyle 24pi \,cm^2$ using the method $\displaystyle \nabla f=\lambda \nabla g \; and \; g(x,y,z)=0$.

My question is that, how come the final result of r and h is min and not max. What if the question ask for the largest surface area in this case?