alleryThe function f(x) = |x| at x = 0 is:
ABoth continuous and differentiable everywhere
BContinuous but NOT differentiable (sharp corner at 0)
CDifferentiable but not continuous in this case
DNeither continuous nor differentiable at this point
Answer & Solution
Correct answer: B. Continuous but NOT differentiable (sharp corner at 0)
|x| is CONTINUOUS at 0 (limit = 0 = f(0)).
**But NOT differentiable:** left-derivative = -1, right-derivative = +1. The graph has a 'kink' at origin.
Continuity does NOT imply differentiability.
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