If f x = - 2 sin x π ≤ x ≤ 3 π 2 p cos x + q 3 π 2 < x < 2 π cos x - 2 2 π ≤ x ≤ 5 π 2 r sin x 5 π 2 < x ≤ 3 π is continuous in π , 3 π , then the number of points at which f x is not differentiable is/are

Step-by-step solution

At 3 π 2 , - 2 - 1 = p 0 + q ⇒ q = 2 At 2 π , p + q = 1 - 2 ⇒ p = – 3 At 5 π 2 , 0 - 2 = r 1 ⇒ r = - 2 f ' x = - 2 c o s x ;     π ≤ x < 3 π 2 N D ;     x = 3 π 2 3 s i n x ;     3 π 2 < x < 2 π 0 ;     x = 2 π - s i n x ;     2 π < x < 5 π 2 N D ;     x = 5 π 2 < x < 3 π - 2 c o s x ;     5 π 2 < x < 3 π &#