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A function f is defined as f(x) = product from k=1 to infinity of (1 + 2*cos(2x / 3^k)) / 3. How many points in the open interval x in (0, 3*pi) are there where f is non-differentiable? (Here [.] denotes the greatest integer function.)

1. 0
2. 1
3. 2
4. 3

Correct answer: 0

Solution

Using the telescoping identity repeatedly, the infinite product simplifies to a smooth function on (0, 3*pi), making it differentiable everywhere in that interval.

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