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Question

The total number of points of non-differentiability of
f(x)=max{sin2x,cos2x,34} in [0,10π], is

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Solution

Since, sin2x and cos2x are periodic with period π and in [0,π], there are four points of non-differentiability of f(x) if we follow the path along max{sin2x,cos2x,34} as it is evident from the graph below.
In [0,10π], there are 40 points of non- differentiability.


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