
The foundations of calculus of variations 23
along with the given boundary condition of
y(x
0
)=y
0
is satisfied, in addition to obeying the constraint of
∂f
∂y
|
x=x
1
=0.
Similar arguments may be applied when the starting point is open. This
problem is the predecessor of the more generic constrained variational prob-
lems, the topic of the next chapter.