Answer: differentiable.
- A differentiable
- B well defined
- C real-valued
- D clearly bounded
Correct answer: A. differentiable
Explanation: It is continuous everywhere but has no derivative at the corner x = 0.
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.