KVPY SX SB Exam 2018 Question Paper

Question : 10 of 120

Marks: +1, -0

Let f(x) = x|sin x|, x ∈ R. Then

Solution:

f(x) = x|sin x| (continuous fucntion)

\f(x)=\{\table x\sin x, x ∈U(2m ,(2m+ 1)π );-x\sin x,x∈ U((2m+ 1) ,(2m +2)π )

critical points are x = nπ

\f'(x)=\{\table \sin x+x\cos x , x ∈U(2mπ ,(2m+ 1)π );-\sin x,x∈ U((2m +1) ,(2m+ 2)π )

LHD ≠ RHD for x = nπ – {0}

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