Answer: x = 0.
- A x = 1
- B x = 0
- C x = −1
- D nowhere
Correct answer: B. x = 0
Explanation: There is a corner at x = 0 where the left and right derivatives differ.
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.