Mathematics for Economists

Homework

Analyze the problems

Z 1

0

x^2 +



x

 2

dt! maxmin , x( (^0) )=x( (^1) )= 0.
Analyze the problems
ZT
0

U



cx e rt



dt, x( 0 )=x 0 ,x(T)= 0

wherecandrandx 0 are positive constants,Uis a continuously

di§erentiable function.

Solve the above problem ifU(z)=ezv/vwherevis a positive

constant.