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The function f(x) = |x| at x = 0 is continuous but not:
ADefined there
BReal valued at
CBounded there
DDifferentiable
Answer & Solution
Correct answer: D. Differentiable
1. The graph of the modulus function has a sharp corner.
2. You can draw it without lifting the pen.
3. But no single tangent exists at the corner.
4. So it is continuous but not differentiable.
_Source: NCERT Class 12 Mathematics, Ch 5 'Continuity and Differentiability'_
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