# 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!!!!!

## Answers and Replies

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Dick
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?

arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
The func is cont. at x=1. Plug in 1 again, in both expression

Whoa! I really feel like an idiot now. I messed up the arithemetic.