MathDB

Let

C

be the class of all real valued continuously differentiable functions

f

on the interval

[0,1]

with

f(0)=0

and

f(1)=1 .

Determine the largest real number

u

such that

u \leq \int_{0}^{1} |f'(x) -f(x) | \, dx

for all

f

C.

Problem Statement