4 Some forms of cost functions Envelope theorem an objective function depend on some parameter M(a)=max f(x, a) Then: d(a of( a e throve x=x(a) lecture 3 for Chu Kechen Honors Collegelecture3 for Chu Kechen Honors College 4.Some forms of cost functions ▪ Envelope theorem: an objective function depend on some parameter. ▪ Then: see the prove. ( ) max ( , ) x M a f x a = ( ) ( ) ( , ) x x a dM a f x a da a =  = 