Consider f(x) = [ 2( x - ^3 x) + | x - ^3 x| 2( x - ^3 x) - | x - ^3 x| ]

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Consider f(x)=[2(sin⁡x−sin⁡3x)+∣sin⁡x−sin⁡3x∣2(sin⁡x−sin⁡3x)−∣sin⁡x−sin⁡3x∣],x≠π2 for x∈(0,π),f(x) = \left[ \frac{2(\sin x - \sin^3 x) + |\sin x - \sin^3 x|}{2(\sin x - \sin^3 x) - |\sin x - \sin^3 x|} \right], \quad x \neq \frac{\pi}{2} \text{ for } x \in (0, \pi), f(π2)=3f\left(\frac{\pi}{2}\right) = 3 where [⋅][\cdot] denotes the greatest integer function, then (1) ff is continuous and differentiable at x=π/2x = \pi/2 (2) ff is continuous but not differentiable at x=π/2x = \pi/2 (3) ff is neither continuous nor differentiable at x=π/2x = \pi/2 (4) None of the above

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