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