Functions 4

  • #1

Homework Statement


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

Homework Equations





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!!!!!
 

Answers and Replies

  • #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?
 
  • #3
arildno
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The func is cont. at x=1. Plug in 1 again, in both expression
 
  • #4
Whoa! I really feel like an idiot now. I messed up the arithemetic.
 

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