Let f x = min 1 , 1 + x sin x , 0 ≤ x ≤ 2 π . If m is the number of points, where f is not differentiable and n is the number of points, where f is not continuous, then the ordered pair m , n is equal to

Step-by-step solution

Given, f x = min 1 , 1 + x sin x x ∈ 0 , 2 π f x = 1 ,    0 ≤ x ≤ π 1 + x sin x , π ≤ x ≤ 2 π Now, at x = π , lim x → π - f x = 1 = lim x → π + f x ∴     f x is continuous in 0 , 2 π So, number of points of discontinuity is zero or n = 0 Now, at x = π L.H.D = lim h → 0 f π - h - f π - h = 0 R.H.D = lim h → 0 f π + h - f π h = lim h → 0 1 - π + h sin h - 1 h = -