(1 point) Use Rolle's Theorem and a proof by contradiction to show that the function f(x) = 2x5 + 2x 10 does not have two real roots. Proof: Suppose f(x) has two real roots a and b such that at) = f(b) = Since the conditions of Rolle's theorem hold true for f on [a, b], there exists at least one number c in the interval (a, b) such that f'(c) = However, the derivative f ' (x) = is always ? v and, therefore, it is ? v for f'(x) = This contradicts the conclusion of Rolle's Theorem and, therefore, f ? v have two real roots