I have the following inequality
where is a continuous differentiable function and is a constant.
My question, what is the upper bound for
where is positive integer larger then 2.
There is no upper bound. Choose a number c such that 0<c<t, let f(x) = M/c when x < c and 0 otherwise. f is not continuous differentiable but one is always able to find a differetiable function F as close as possible to f. Now , and . Choose a small c you can get an arbitary big result.