Find the points where the function is not differentiable

Abdul Quadeer

1. The problem statement, all variables and given/known data
Find the points where the function given by

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.

micromass

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...

Abdul Quadeer

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

micromass

-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...