Q.

Which of the following statements are CORRECT (where {.} denotes the fractional part of the function)

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a

f(x)=||x2||x6||3|x|+2x+1 is not differentiable at 4 points

b

f(x)={x} |cosπx| is not differentiable for all integers 

c

f(x)=|cosx|sin1(sinx) is differentiable for all  x(0,2π)

d

f(x)={x}sin2((2x12)π) is differentiable for all integers

answer is A, C, D.

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Detailed Solution

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A. f(x)={x}cos2πx is diff for all integers
B.  f(x)=|cosx|sin1(sinx)|is  not  diff  at  x=π2  
C.  f(x) is not diff at (0,2,6,4)
D. f(x)={x}(cosπx) is not diff for all integers

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