# Find the points where the function is not differentiable

1. ### zorro

1. The problem statement, all variables and given/known data
Find the points where the function given by
$image=http://latex.codecogs.com/gif.latex?f(x)=&space;\left&space;(&space;x^{2}-1&space;\right&space;)\left&space;|&space;x^{2}-3x+2&space;\right&space;|+cos\left&space;|&space;x&space;\right&space;|&hash=af78a5c5f3cd719af2a3e61d346e687b$
is not differentiable.

3. The attempt at a solution

I got the doubtful points as +-1, 2
How do I check the differentiability now? The mod. function is confusing me a bit.

2. ### micromass

19,798
Staff Emeritus
You should transform this function in a piecewize function.

That is, the doubtfull points are those when x2-3x+2=0 and x=0.
Once you've determined these points, you can write your function is piecewise form...

3. ### zorro

My book says 1,-1,2 are the possible points of non-differentiability.
Can you tell me how -1 is included?
Moreover, 0 as you told would not be a doubt full point as cos(modx) is same as cosx

4. ### micromass

19,798
Staff Emeritus
-1 is not a point of non-differentiability, at least not if you follow my method. Maybe the book uses other methods.

You are correct about 0. Thus 1 and 2 are the only possible points of non-differentiability...