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Rolle's theorem is the special case of the mean value theorem where f(a) = f(b). Then the secant is horizontal, so some interior point must have a horizontal tangent.
Rolle's theorem
if f(a) = f(b) then f'(c) = 0 for some c in (a, b)
The polynomial factors as x(x − 2)(x − 3), so f(2) = f(3) = 0 and Rolle applies; f' = 3x² − 10x + 6 vanishes at x ≈ 2.5486.
Because |x| on [−1, 1] has f(−1) = f(1) but no horizontal tangent — the corner at zero breaks the theorem.