# Find the points where the function is not differentiable

by zorro
Tags: differentiable, function, points
 P: 1,395 1. The problem statement, all variables and given/known data Find the points where the function given by $f(x)=&space;\left&space;(&space;x^{2}-1&space;\right&space;)\left&space;|&space;x^{2}-3x+2&space;\right&space;|+cos\left&space;|&space;x&space;\right&space;|$ 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.
 Mentor P: 16,692 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...
 P: 1,395 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
Mentor
P: 16,692

## Find the points where the function is not differentiable

-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...

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