Answer: 2.
- A 1
- B 2
- C 3
- D 0
Correct answer: B. 2
Explanation: It jumps at the integers 1 and 2 inside the interval, giving 2 points.
f(x)=|x| is perfectly continuous at x=0 (no break, no jump), but the curve has a sharp corner there: approaching from the left gives slope -1 and from the right gives slope +1 - since these one-sided derivatives disagree, the function is not differentiable at that point.
Concept context
When a function has no breaks (continuity) and when it has a well-defined slope (differentiability), plus rules for differentiating implicit, inverse trig, exponential, log, and parametric functions.