Using Theorem 1, prove that if F'(x) = (x), where is a polynomial of degree n 1, then F is a polynomial of

Using Theorem 1, prove that if F'(x) = ƒ(x), where ƒ is a polynomial of degree n − 1, then F is a polynomial of degree n. Then prove that if g is any function such that g⁽ⁿ⁾(x) = 0, then g is a polynomial of degree at most n.

THEOREM 1 The General Antiderivative Let y = F(x) be an antiderivative of y = f(x) on (a, b). Then every antiderivative on (a,b) is of the form y = F(x) + C for some constant C.