# 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

#### Answer:

FALSE.

Counter-example:

The derivatives of both functions are the same:

and yet,

#### Explanation:

Given a derivative **"a version"** of the original function

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,