Limit Definition of Derivative

[cjaylee]

Homework Statement

Use the limit definition of derivative to determine the derivative of the following function:

f(x) = { sqrt(x^2+1) if x<=0
0 if x>0

Homework Equations

I'm not sure as to why the function is not continuous at x=0, and so it's not differentiable at that point.

The Attempt at a Solution

The left-hand limit and right-hand limit give me 0. And if I plot a graph, the graph hits 0 as it moves from one function to the other.

 

[HallsofIvy]

The left hand limit is "1", not "0"! I would think that would be obvious. What is f(-0.001)?