Monotonicity — increasing and decreasing functionsHard

Intervals of Increasing and Decreasing Functions

Let (2, 3) be the largest open interval in which the function f(x) = 2 log_e(x – 2) – x² + ax + 1 is strictly increasing and (b, c) be the largest open interval, in which the function g(x) = (x – 1)³(x + 2 – a)² is strictly decreasing. Then 100(a + b – c) is equal to :

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