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Branch function

  1. Feb 15, 2005 #1
    Let f(x) be a function defined by:

    f(x)= { 2x+1 for x (less than or equal to) 2
    .5x + k for x (greater than) 2

    A) For what value of 'k' will f(x) be continuous at x=2? Justify your answer.
    B) Using the value of 'k' found in part A, determine whether f(x) is differentiable at x=2.


    Any help on where to get started would be great. I think I have to plug in the 2 in the first equation...but I'm lost on what to do. Thanks.
     
  2. jcsd
  3. Feb 15, 2005 #2

    Hurkyl

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    The definitions are usually a good place to start when you don't know what to do. What does it mean for this particular function to be continuous at 2?
     
  4. Feb 15, 2005 #3

    mathwonk

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    and remember to think about both right and left hand limits in defining continutity.
     
  5. Feb 15, 2005 #4

    dextercioby

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    And remember to make the distinction between right and left when discussing differentiability...

    I think you got enough clues...:wink:

    Daniel.
     
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