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

Question

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,

MARKS App · Accepted Answer

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 ⇒ f x is not differentiable at 3 π 2 & 5 π 2

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