Results 1 to 4 of 4

Math Help - Differentiability

  1. #1
    Member
    Joined
    Oct 2007
    Posts
    178

    Differentiability

    Find all values of x for which the function is differentiable.

    P(x)= sin(|x|)-1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,817
    Thanks
    316
    Awards
    1
    Quote Originally Posted by Truthbetold View Post
    Find all values of x for which the function is differentiable.

    P(x)= sin(|x|)-1
    Can you think of any points of the graph of y = |x| where the function isn't differentiable?

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2007
    Posts
    178
    Quote Originally Posted by topsquark View Post
    Can you think of any points of the graph of y = |x| where the function isn't differentiable?

    -Dan
    To shorten the below: no.

    If something is not differentiable only when it at the very middle (where the right and left come together, usually in examples as (0,0,) of cusps, corners, vertical tangents, and a non-removable discontinuity, then I cannot think or see, using a graphing calculator, any points.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,817
    Thanks
    316
    Awards
    1
    Quote Originally Posted by Truthbetold View Post
    To shorten the below: no.

    If something is not differentiable only when it at the very middle (where the right and left come together, usually in examples as (0,0,) of cusps, corners, vertical tangents, and a non-removable discontinuity, then I cannot think or see, using a graphing calculator, any points.
    f(x) = |x|

    Consider x near 0. When x approaches 0 from the left, the first derivative is -1. When x approaches 0 from the right, the first derivative is 1. So the derivative of |x| does not exist at x = 0.

    We can make a similar argument for f(x) = sin(|x|) - 1. See the graph below. Notice the cusp at x = 0.

    -Dan
    Attached Thumbnails Attached Thumbnails Differentiability-cusp.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. differentiability
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 16th 2012, 06:31 AM
  2. Differentiability
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 13th 2010, 11:45 AM
  3. Differentiability
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 21st 2010, 07:16 PM
  4. Differentiability
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 20th 2009, 11:14 AM
  5. Differentiability
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 30th 2008, 01:08 PM

Search Tags


/mathhelpforum @mathhelpforum