Mathematics for Economists

Homework

Find the extremal solutions

Zb

a

xy^0 +

y^0

2

dx

Find the extremal solutions

Zπ

0

4 xcost+x

2

x^2 dt, x( (^0) )=x(π)= 0.
Show that the linear functional
Zb
a
a(t)x(t)+b(t)x(t)+c(t)dt,
wherebandcare continuous anda 6 =0 is continuously di§erentiable
has no extremal solution.