Find the number of points where the function f(x) = |x| + |x/3 - 1| + |x| - |x/3 - 1| is non-differentiable.

Correct answer: 1

Solution

f(x) = |x| + |x/3 - 1| + |x| - |x/3 - 1| = 2|x|. The |x/3-1| terms cancel exactly. So f(x) = 2|x|, which is differentiable everywhere except x = 0. At x = 0, f(x) = 2|x| is non-differentiable. So the number of non-differentiable points = 1.

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