2.I.5D2 . \mathrm{I} . 5 \mathrm{D} \quad

Methods
Part IB, 2008

Describe briefly the method of Lagrange multipliers for finding the stationary values of a function f(x,y)f(x, y) subject to a constraint g(x,y)=0g(x, y)=0.

Use the method to find the largest possible volume of a circular cylinder that has surface area AA (including both ends).