Mathematics for Economists

Calculus of variations

λ^2  λx

1 +



x

 2 ^3 /^2



x

 2

1 +



x

 2

x



1 +



x

 2 ^3 /^2 

vu

uu

uu

t

x^2



1 +



x

 2  3 +^4



x

 2

1 +



x

 2

so the roots are positive and negative, so the functionF



t,x,x



is not

convex in



x,x



.