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MHT CET202618 April 2026Evening ShiftMathematicsDifferentiationActual

If f : R R is an even function then

Options

  1. Af'(0) = 1
  2. Bf'(x) is an even function
  3. Cf(0) = 0
  4. Df'(x) is an odd function

Correct answer

D. f'(x) is an odd function

Step-by-step solution

Given that f(x) is an even function, we have: f(-x) = f(x) Differentiating both sides with respect to x , we get: -f'(-x) = f'(x) f'(-x) = -f'(x) This condition satisfies the definition of an odd function. Therefore, f'(x) is an odd function. Answer: f'(x) is an odd function

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