Mathematics · Calculus

If the function f is given by f(x) = x3 - 3(a - 2)x2 + 3ax + 7, for some a ∈ ℝ, is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation f(x) - 14(x - 1)2 = 0 (where x ≠ 1) is: