Let f(x)=sin⁡x2−5x+6×2−5x+6x≠2,31x=2 or 3the set of all points where f is differentiable is 

Let f(x)=sinx25x+6x25x+6x2,31x=2 or 3

the set of all points where f is differentiable is

 

  1. A

    (,)

  2. B

    (,)~{2}

  3. C

    (,)~{3}

  4. D

    (,)~{2,3} or R-2,3

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    Solution:

    The function is clearly differentiable except 

    possibly at x=2,3

    f(2+)=limh0+f(2+h)f(2)h=limh0+sinh(1h)+h(1h)h2(1+h)=limh0+sinh(1h)h(1h)+11h

    The last limit doesn’t exist. If this limit then limh0+1h exist, 

    which is not true

    Thus f is not differentiable at x=2 . Similarly f is not dif-

    ferentiable   at x = 3. Hence the set of all points where f is 

    (,)~{2,3}

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