Answer: x = 2.
- A x = 0
- B x = 1
- C x = 2
- D f is differentiable everywhere
Correct answer: C. x = 2
Explanation: Similar to |x| shifted, |x-2| has a sharp corner at x = 2 where the left and right derivatives (-1 and +1) disagree.
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.