Mathematics for Economists

Calculus of variations

Example

Solve the problem

Z 2

0

( 4  3 x^2  16

.

x 4 x^2 )etdt!max

x( 0 )= 8 / 3 ,x( 2 )= 1 / 3

In this case

F(t,x,x.)=( 4  3 x^2  16 x 4 x

2

)et

Fx^0 = 6 xet,Fx^0 =



 16  8 x



et.