1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?