Let f : R → R be differentiable at c ∈ R and f(c) = 0. If g(x) = |f(x)|, then at x = c, g is:

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JEE Mains Previous Paper 1 (Held On: 10 Apr 2019 Shift 1)
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  1. Not differentiable if f'(c) = 0
  2. Differentiable if f'(c) ≠ 0
  3. Differentiable if f'(c) = 0
  4. Not differentiable

Answer (Detailed Solution Below)

Option 3 : Differentiable if f'(c) = 0
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JEE Main 04 April 2024 Shift 1
90 Qs. 300 Marks 180 Mins

Detailed Solution

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Since, f(c) = 0

Then, 

 if f(x) > 0

and ; if f(x) < 0

⇒ g'(c) = f'(c) = -f'(c)

= f'(c) + f'(c)

⇒ 2f'(c) = 0

⇒ f'(c) = 0

Hence, g(x) is differentiable if f'(c) = 0

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