alleryDoes continuity at a point guarantee differentiability?
AYes, it always
BOnly at zero p
COnly for lines
DNo, not always
Answer & Solution
Correct answer: D. No, not always
1. Theorem 3 runs one way only.
2. The modulus function at 0 is the standard counter-example.
3. So continuity does not guarantee differentiability.
4. The answer is no, not always.
_Source: syllabus Mathematics, Ch 5 'Continuity and Differentiability'_
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