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Derivative of Piece-wise Function

Prove the following:

If f(x) = 1 if x is greater than or equal to 0 and f(x) = 0 if x < 0, then there is no function F such that F'(x) = f(x) for every x in R.

See #9 in the attached file.


Solution Preview

Let's look at the case of x = 0. (Since we want to disprove that there is a function F with F'(x) = f(x) for all x in R, it is enough to show that there is no ...

Solution Summary

The solution uses the definition of derivative to prove the statement.