- #1
Bashyboy
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Homework Statement
I am trying to prove without using the mean value theorem that two different functions with the same derivative differ only by a constant. Is it possible to do this without the mean value theorem? If so, would someone help guide me towards the right solution.
Homework Equations
The Attempt at a Solution
Let ##f'(x) = h(x)## and ##g'(x) = h(x)##. Define the function ##T(x) = h(x) - g(x)##, which has the derivative ##T'(x) = 0## for all ##x##. If I could prove that the derivative of a function being identically zero implies that the function is a constant, then I would be finished; however, even this is giving trouble.