Answer: f(a).
- A f(a)
- B 0
- C infinity
- D 1
Correct answer: A. f(a)
Explanation: Continuity requires the limit at a to exist and equal the function value f(a).
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.