Let f(x) = x2 - 5 x + 4
(a) Since every polynomial is a continuous function for every value of x
∴ f is continuous in [1, 4]
(b) f'(x) = 2 x - 5, which exists in (1, 4)
∴ f is derivable in (1, 4)
(c) f(1) = 1 - 5 + 4 = 0
f(4) = 16 - 20 + 4 = 0
∴ f(1) = f(4)
∴ f satisfies all the condition of Rolle's Theorem
∴ there must exist at least one value c of x such that f'(c) = 0 where 1 < c < 4
∴ Rolle's theorem is verified.