Let f : R → R be a function defined by : f x = max t ≤ x t 3 - 3 t ; x ≤ 2 x 2 + 2 x - 6 ; 2 < x < 3 x - 3 + 9 ; 3 ≤ x ≤ 5 2 x + 1 ; x > 5 Where t is the greatest integer less than or equal to t . Let m be the number of points where f is not differentiable and I = ∫ - 2 2 f x d x . Then the ordered pair m , I is equal to

Step-by-step solution

f x = x 3 - 3 x , x ≤ - 1 2 , - 1 < x ≤ 2 x 2 + 2 x - 6 , 2 < x < 3 9 , 3 ≤ x < 4 10 , 4 ≤ x < 5 11 , x = 5 2 x + 1 , x > 5 Clearly f x is not differentiable at x = 2 , 3 , 4 , 5 ⇒ m = 4 I = ∫ - 2 2 f x d x = ∫ - 2 - 1 x 3 - 3 x d x + ∫ - 1 2 2 · d x = 27 4 Hence the ordered pair is 4 , 27 4