Calculus problem

[Steven G]

Suppose for some function f⁽ⁿ⁾(x)=0.
By repeated integration, you can show that f(x) is a polynomial.
Is there another proof showing this result? Can I please see it?

 

[lex]

Would you be happy integrating once?
In which case induction on n. (f'(x) would be a polynomial, so f(x) would be too).