Find the value of c in Rolle's theorem for the function f(x) = x³ in [−√3, 0].

Let f be continuous on a closed interval [a, b] and differentiable on the open interval (a, b). If f(a) = f(b), then there is at least one point c in (a, b) where f'(c) = 0.
Given f = x³ in [−√3, 0] ⇒ f'(x) = 3x² ⇒ f'(c) = 3c² ⇒ 0 ⇒ c² = 0 ⇒ c = 0 as c is in [−√3, 0]