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Essentially, I am attempting to extend a proof which uses f(x) where f''(x) is defined. I would like to extend this proof to a piecewise-constant f(x). However, one of the requirements is that f'(x) >> f''(x) >> f

^{(n)}(x). If H''[(0)] is undefined, than this approach will not work.

My attempt at a solution is as follows. Given a general, differentiable function f(x), then

[itex]\int[/itex]f(x)δ

^{(n)}dx [itex]\equiv[/itex] -[itex]\int[/itex][itex]\frac{∂f}{∂x}[/itex]δ

^{(n-1)}(x)dx

I am, however, unclear as to the meaning of δ

^{(n-1)}, especially when n=1.

Thanks for your help.