# Thread: Showing there is no anti-derivative for piecewise function?

1. ## Showing there is no anti-derivative for piecewise function?

I am having difficulty with this question. I think the problem im having is showing how the antiderivative does not exist ( for example what are the requirements needed for it not to exist). The second problem I have is that im not sure how to solve these type of questions when given piecewise functions.

The question states:" show that the function f(x)=x for x less than or equal to 0 and f(x)=1 for greater than 0 has no antiderivative on R. Hint find a potential antiderivative F of f and show that F has no derivative at 0."

Any help would be greatly appreciated

2. This problem is very similar to the other thread that I just answered.

3. Originally Posted by Solid8Snake
I am having difficulty with this question. I think the problem im having is showing how the antiderivative does not exist ( for example what are the requirements needed for it not to exist). The second problem I have is that im not sure how to solve these type of questions when given piecewise functions.

The question states:" show that the function f(x)=x for x less than or equal to 0 and f(x)=1 for greater than 0 has no antiderivative on R. Hint find a potential antiderivative F of f and show that F has no derivative at 0."

Any help would be greatly appreciated
Looks like you just need to follow the hint! Can you find an anti-derivative for $f(x)= x$? Can you find an anti-derivative form $f(x)= 1$?