# How to find whether this function is differentiable

1. Nov 3, 2008

### lax1113

1. The problem statement, all variables and given/known data
F(x)= {1/2x+1 when x=<2
{squareroot(2x) when x=>/=2

is it differentiable at x=2.

2. Relevant equations
(f(x)-f(2))/(x-2)

3. The attempt at a solution
So i know i ahve to take the limit from both the negative and positive of 2, and determine if they are equal. But after pluggin everyting in i get 0/0 for both equations, and i tried to change the equations a little bit to see if they could reveal the limit, but i coudln't figure it out.

2. Nov 3, 2008

### Dick

Re: differentibility

You ALWAYS get a 0/0 limit when you apply the definition of derivative. You have to do some algebra to fix that. What form did you get for one of the limits and how did you try to 'fix' it so you get a finite limit?

3. Nov 4, 2008

### lax1113

Re: differentibility

Hey dick,
Thanks for posting. I went back again a little bit after and it seemed really obvious. I hate how sometimes ill stare at a problem that is very simple and just dont get it, but then i revisit for 2 seconds and it jumps out at me.

I got them to each equal 1/2 after changing them algebraically.