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Homework Help: Functions 4

  1. Mar 1, 2007 #1
    1. The problem statement, all variables and given/known data
    f(x) is a piecewise function defined as:

    [tex]|x-3| x>=1[/tex]
    [tex]\frac{x^2}{4}-\frac{3x}{2}+\frac{13}{4} x<1[/tex]

    Discuss the continuity and differentiability of this funtion at x=1 and x=3
    2. Relevant equations



    3. The attempt at a solution
    At x=3, this function is continuous but not differentiable, being a modulus funtion. But how is is continuous and differentiable at x=1? Putting limit x=1 in the above funtion doesnt give you the same value for both the parts!!!!!
     
  2. jcsd
  3. Mar 1, 2007 #2

    Dick

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    Look at the limit as x->1 from both sides of the function and the derivative of the function. What do you get as answers to these four questions?
     
  4. Mar 2, 2007 #3

    arildno

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    The func is cont. at x=1. Plug in 1 again, in both expression
     
  5. Mar 4, 2007 #4
    Whoa! I really feel like an idiot now. I messed up the arithemetic.
     
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