# Calculus of Variations by Charles Fox: Question on Statement in Section 2.4

Fox states in Section 2.4, pg. 38, that

"Anticipating this result, it follows that even if $$u(x)$$ vanishes at either or both of the values $$x=a$$ and $$x=b$$, both $$t^2(a)/u(a)$$ and $$t^2(b)/u(b)$$ still vanish since $$t(a)=t(b)=0$$ by hypothesis."

How does this make sense? The quotient would become $$0/0$$ in such a case, which is indeterminate, not vanishing.

• @Cesareo Any ideas? – A. Hendry Mar 21 at 23:41

I'm just going to assume the Jacobi Necessary Condition is only looking at the internal interval $$(a,b)$$ and call it a day.

EDIT 3-25-19:

This is true (the necessary condition looks only at the open interval). Hence, Fox's statement is ultimately incorrect IFF $$u$$ were to equal $$0$$ at any point, but this is not possible (see Difficulty Understanding Sufficient Conditions for Weak Extrema in Calculus of Variations).