585.

It is a polynomial in x.
(i) since every polynomial in x is a continuous function for every value of x
∴ f(x) is continuous in [0, 8]
(ii) f'(x) = 8 - 2 x, which exists in (0, 8)
∴ f(x) is derivable in (0, 8)
(iii) f(0) = 0 - 0 = 0
f(8) = 8 (8) - (8)² = 64 - 64 = 0
∴ f(0) = f(8)
∴ f(x) satisfies all the conditions of Rolle's theorem.
∴ there must exist at least one value c of x such that f'(c) = 0 where 0 < c < 8.
Now f'(c) = 0 gives 8 - 2 c = 0 ⇒ c = 4 ∈ (0, 8)
∴ Rolle's theorem is verified.