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The function f is defined on [-1, 2] as follows: - f(x) = |sin(pi*x)| for -1 <= x < 0 - f(x) = 1 - {x} for 0 <= x < 1 (where {x} denotes the fractional part) - f(x) = 1 + [cos(pi*x/2)] for 1 < x <= 2 (where [x] denotes the greatest integer function) and f(1) = 0. At how many points in [-1, 2] is f continuous but not differentiable?

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

Correct answer: 3

Solution

By checking each boundary and critical interior point carefully, we find exactly 3 points where f is continuous but the left-hand and right-hand derivatives differ, making f non-differentiable there.

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