594. Verify Roll�s Theorem for the function :f(x) = log (x² + 2) - log 3 in [-1, 1]

Let f(x) = log (x² + 2) - log 3
(a) Since log (x² + 2) and log 3 are both continuous in [-1, 1]
∴ 1og (x² + 2) - log 3 is continuous in [-1, 1] ⇒ f is continuous in [-1, 1]

∴ f is derivable in (-1, 1).
(c) f(-1) = log (1 + 2) - log 3 = 0
f(1) = log (1 + 2) - log 3 = 0
∴ f(-1) = f(1)
∴ f satisfies all the conditions of Rolle's Theorem
∴ there must exist at least one value c of x such that f'(c) = 0 where - 1 < c < 1

∴ Rolle's Theorem is verified.