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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2013 · Mathematics · Continuity and Differentiability

Consider the function f(x)=\ array cc x^2, & x > 2 3 x-2, & x ≤ 2...

Consider the function f(x)=\left\{x2,x>23x−2,x≤2\begin{array}{cc}x^2, & x > 2 \\ 3 x-2, & x \leq 2\end{array}\right.. Which one of the following statements is correct in respect of the above function?

Options

  1. Af(x)f(x) is derivable but not continuous at x=2x=2.
  2. Bf(x)f(x) is continuous but not derivable at x=2x=2.
  3. Cf(x)f(x) is neither continuous nor derivable at x=2x=2.
  4. Df(x)f(x) is continuous as well as derivable at x=2x=2.

Correct answer

B. f(x)f(x) is continuous but not derivable at x=2x=2.

Step-by-step solution

Let f(2+h)=4f(2+h)=4 \quad as h→0h \rightarrow 0 Let f(2−h)=4f(2-h)=4 \quad as h→0h \rightarrow 0 Let f(2)=4f(2)=4 continuous at $x=2f^{\prime}\left(2^{+}\right)=4, f^{\prime}\left(2^{-}\right)=3
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