# Homework Help: Functions 4

1. Mar 1, 2007

### chaoseverlasting

1. The problem statement, all variables and given/known data
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
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. Mar 1, 2007

### Dick

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. Mar 2, 2007

### arildno

The func is cont. at x=1. Plug in 1 again, in both expression

4. Mar 4, 2007

### chaoseverlasting

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