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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2016 · Mathematics · Continuity and Differentiability

Paragraph: Let f(x)=\ array ll -2, & -3 ≤ x ≤ 0 x-2, & 0 Question:...

Paragraph: Let \mathrm{f}(\mathrm{x})=\left\{−2,−3≤x≤0x−2,0<x≤3\begin{array}{ll}-2, & -3 \leq \mathrm{x} \leq 0 \\ \mathrm{x}-2, & 0 < \mathrm{x} \leq 3\end{array}\right. and g(x)=f(∣x∣)+∣f(x)∣\mathrm{g}(\mathrm{x})=\mathrm{f}(|\mathrm{x}|)+|\mathrm{f}(\mathrm{x})|
Question: What is the value of the differential coefficient of g(x)g(x) at x=−2x=-2 ?

Options

  1. A−1-1
  2. B00
  3. C11
  4. D22

Correct answer

B. 00

Step-by-step solution

⇒LHD≠RHD\Rightarrow \mathrm{LHD} \neq \mathrm{RHD} Thus g(x)g(x) is not differentiable at x=2x=2.
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