The set of points where the function f(x)=[x]+|1−x|,−1≤x≤3where [.]  denotes the greatest integer function, is not differentiable, is 

The set of points where the function f(x)=[x]+|1x|,1x3

where [.]  denotes the greatest integer function, is not differentiable, is 

  1. A

    {1,0,1,2,3}

  2. B

    {-1,0,2}

  3. C

    {0,1,2,3,}

  4. D

    {-1,0,1,2}

    Register to Get Free Mock Test and Study Material

    +91

    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    We have

    f(x)=x,    1x<01x,    0x<1x,    1x<21+x,    2x<35,    x=3

    Clearly, f (x) is discontinuous at x = 0,1, 2, and 3.

    So, it is not differentiable at these points.

    At x=-1, we have

    limx1+f(x)=limx1+x=1=f(1)

    So, it is continuous at x=-1.

    Also, (RHD at x=-1)=-1 (a finite number). 

    Therefore, f (x) is differentiable at x=-1.

    Chat on WhatsApp Call Infinity Learn

      Register to Get Free Mock Test and Study Material

      +91

      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.