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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2018 · Mathematics · Continuity and Differentiability

For the function f(x)=|x-3| , which of the following is not correct?

For the function f(x)=∣x−3∣f(x)=|x-3|, which of the following is not correct?

Options

  1. AThe function is not continuous at x=−3x=-3
  2. BThe function is continuous at x=3x=3
  3. CThe function is differentiable at x=0x=0
  4. DThe function is differentiable at x=−3x=-3

Correct answer

A. The function is not continuous at x=−3x=-3

Step-by-step solution

\begin{gathered} f(x)=|x-3| \\ \Rightarrow \quad f(x)=\begin{cases}(x-3), & x \geq 3 \\ (3-x), & x < 3\end{cases}\\ f^{\prime}(x) \text{ at } x=3^{+}=1 \\ f^{\prime}(x) \text{ at } x=3^{-}=-1 \end{gathered} Thus, f(x)f(x) is not differentiable at x=3x=3 but f(x)f(x) is continuous at x=3x=3.
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