Analyzing Continuity and Differentiability of f(x) at x=1 & x=3

[chaoseverlasting]

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

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 doesn't give you the same value for both the parts!

 

[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?

 

[arildno]

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

 

[chaoseverlasting]

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