Answer: (b − a).
- A (b − a)
- B (a − b)
- C (b + a)
- D ab
Correct answer: A. (b − a)
Explanation: The MVT equates the derivative at some c to the average rate of change over [a, b].
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.