Short and efficient method to find number of points of non differentiablilty of a function

I get very confused in such type of questions and atleast 1 such question is coming in all the tests i have given in numerical type section…
Not the normal functions but the ones which contain modulus, GIF, fractional part etc etc… ( and the types in which there many modulus functions)
For example…


@Seshank
@manan_uppadhyay
@Sanjay_S
@anon83175304_lavesh
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Dude @Navjeet_Kohli always the most efficient method is to ::
1.Break the given expression into two seperate functions [ if possible]
2.Draw the seperate the graphs of them
3.Find the sharp points as those points are POINTS OF DISCONTINUITY /NON-DIFFERENTIABILITY

lets take your question::
image
image

Hope you got it!!

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yeah @Harish_R is right this is the only way to do

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dude period of cos(pix) is 2,so try to plot yourself and i think u will getting something like this:

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Thanks! Got it!!
Do you have a overview of all the graphical transformations??

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nope i dont have,but i would recommend you to study from Arihant …it is really good (focus more on |f(x)| and f(|x|) .

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there’s this book called playing with graphs in arihant I learnt from it at a very early stage it made by to get a good hold on graphs

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