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If F'(x) = f(x), and G'(x) = f(x), then G(x)=F(x)+c for some constant c

Proof:

(G-F)'=f-f=0

Recall that we proved as a corollary of the Mean Value Theorem that if a function has a derivative zero the it is constant. Hence G(x)-F(x) = c ( for some constant c). That is, G(x)=F(x)+c.

I find that I don't really understand yet what is meant by the above theorem. I think perhaps I might understand it better if I could see an example.

Thank You...