Question
Find the number of points at which the function $f(x)=\max .\{a-x, a+x, \mathrm{~b}\} ;-\infty<x<\infty, 0<a<b$cannot be differentiable.
Step 1
We know that each of these functions is linear and therefore differentiable everywhere. The only points where $f(x)$ could potentially be non-differentiable are the points where two of these functions intersect, as the max function will "switch" from one function Show more…
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