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NDA2021MathematicsContinuity and DifferentiabilityActual

If f(x)=e^ |x| , then which one of the following is correct?

Options

  1. Af^ (0)=1
  2. Bf^ (0)=-1
  3. Cf^ (0)=0
  4. Df^ (0) does not exist

Correct answer

D. f^ (0) does not exist

Step-by-step solution

aligned & f(x)=e^ |x| & f^ (x)=e^x, x 0 aligned gathered =-e^ |x| , x 0 _ x 0⁺ f^ (x) _ x 0⁻ f^ (x) gathered f^ (x) does not exist at x=0

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