Homework Help: Finding the particular anti derivative when given f'(x) and TWO f(value)s

1. The problem statement, all variables and given/known data

Here is the question directly from the book:

f'(x)=x^(-1/3), f(1)=1, f(-1)=-1, find f(x).

2. Relevant equations



3. The attempt at a solution

So there are about ten of these types, and I am very confused. I am confused because if you solve for f(x) with f(a) you get a different value for c than if you solved for f(b).

So finding f(x) I get f(x)=(3/2)x^(2/3) + c
If I make f(x)=1 and x=1, I get the value of c to be -1/2
But if I make f(x)=-1 and x=-1, I get the value of c to be -5/2..

Thank you so much for your help in advance!

 

So whenever f'(0)=DNE, the function f(x) can be written as a piecewise function?

 

OK, thanks again! You helped tremendously.