Problem 11 (Calculus of Variations, bonus) (a) Derive the formula for the area of the surface of rotation determined by rotating the graph of a real valued function u : [a, b] -> R about the domain aris. (b) Call the area calculated in part (a) the Bliss functional A : A - R where A = {uE C'[a, b] : u(a) = d, u(b) = d}. Calculate the first variation of A and determine the first order necessary con- dition for minimizers. (c) What can you say about the minimizers for this