# Functions 4

## Homework Statement

f(x) is a piecewise function defined as:

$$|x-3| x>=1$$
$$\frac{x^2}{4}-\frac{3x}{2}+\frac{13}{4} x<1$$

Discuss the continuity and differentiability of this funtion at x=1 and x=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!!!!!

Dick
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?

arildno