If f‘(x) = g‘(x), then f(x) = g(x). Explain your answer if it is true. If false, provide a counterexample. True or False?
1 Answer
FALSE.
Counter-example:
The derivatives of both functions are the same:
and yet,
Explanation:
Given a derivative
For example, if
then, the anti-derivative is:
where
So, there is no guarantee that you will arrive to the same function every time, and the statement in question is FALSE.
Here's a counter-example:
Let
The derivatives of both functions are the same:
and yet,