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Differentiability: Differentiability at a point MCQ

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Differentiability at a pointHardQuestion 360008

Question

f(x) = |x| is not differentiable at x = 0 because:
  1. A
    LHD ≠ RHD at x = 0 (−1 ≠ +1)
    Correct
  2. B
    f(0) is undefined
  3. C
    f is discontinuous at 0
  4. D
    f'(0) = ∞

Correct answer

LHD ≠ RHD at x = 0 (−1 ≠ +1)

Explanation

Left derivative: lim(h→0⁻) (|h|−0)/h = −1. Right derivative: lim(h→0⁺) h/h = +1. LHD ≠ RHD → not differentiable at x = 0 (though f is continuous there).

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