Hi, I need help with the following problem.

Suppose that and are real valued functions on having period 1 and having continuous first derivatives.

(a) Prove that for some non-negative .

(b) Prove that there is a smallest such value of c.

I proved part a by letting h=f-g, looking for h'=0 and using the mean value theorem, but I can't seem to figure out part b.

Any help would be appreciated.