# If there was a hole in the line at (2,3) and there is another point at (2,1), then would the graph be differentiable at that point and why?

##### 1 Answer

Sep 5, 2016

If I understand the description correctly, the answer is no and the reason is below.

#### Explanation:

The short answer is that the function you have described is not continuous at

**Longer answer**

"A hole in the line at

The point at

Now

# = lim_(xrarr2)(f(x)-1)/(x-2)#

This limit has the form

Since the derivative **is** the limit, the derivative also does not exist.