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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2021 · Mathematics · Continuity and Differentiability

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

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

Options

  1. Af′(0)=1f^{\prime}(0)=1
  2. Bf′(0)=−1f^{\prime}(0)=-1
  3. Cf′(0)=0f^{\prime}(0)=0
  4. Df′(0)f^{\prime}(0) does not exist

Correct answer

D. f′(0)f^{\prime}(0) does not exist

Step-by-step solution

f(x)=e∣x∣f′(x)=ex,x>0\begin{aligned} & f(x)=e^{|x|} \\ & f^{\prime}(x)=e^x, x > 0\end{aligned}\begin{gathered}=-e^{|x|}, x < 0 \\ \lim _{x \rightarrow 0^{+}} f^{\prime}(x) \neq \lim _{x \rightarrow 0^{-}} f^{\prime}(x)\end{gathered}\therefore f^{\prime}(x)doesnotexistatdoes not exist atx=0$
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