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Pietro K.C.
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 Derivative goes to zero   « on: Sep 29th, 2002, 10:43am » Quote Modify

Suppose f(t) is a continuously once-differentiable strictly decreasing positive function for all t >= 0 . Must the derivative f'(t) = 0 as t approaches infinity? Why?
// modified post to include problem statement at top - willywutang 5/21/2008

Hint:
 hidden: not necessarily.

Further hint:
 hidden: for a function g(t) to have zero as a limit at infinity, it means that, given any r > 0, there exists an M > 0 such that |g(t)| < r for *EVERY* t > M.