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## 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!!!!!