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Given a piecewise, prove that it is continous and differentiable

  1. Dec 1, 2011 #1
    1. The problem statement, all variables and given/known data
    For f(x)= { sin(x)/x if x≠0 , 1 if x=0. (a) Show that f is continous and differentiable for all x. (b) Show the derivative f'(x) is continous.


    2. Relevant equations



    3. The attempt at a solution
    I know that if f is differentiable it is continous, so I need to focus on x=0 to show that the function is differentiable. And now I'm stuck lol
     
  2. jcsd
  3. Dec 2, 2011 #2

    HallsofIvy

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    Well, what have you done? What does the "difference quotient" at x= 0?
     
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