Prove that (x) = x 4 + 5x 3 + 4x has no root c satisfying c

Prove that ƒ(x) = x⁴ + 5x³ + 4x has no root c satisfying c > 0. x = 0 is a root and apply Rolle’s Theorem.

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THEOREM 4 Rolle's Theorem Assume that f is continuous on [a, b] and differen- tiable on (a, b). If f(a) = f(b), then there exists a number c between a and b such that f'(c) = 0.