Answer: sharp corner.
- A sharp corner
- B smooth curve
- C flat line
- D single point
Correct answer: A. sharp corner
Explanation: A corner (as in |x| at 0) makes a function continuous yet not differentiable there.
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.