If f(x) = |x − 2|, then f'(2) equals :

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RPSC 2nd Grade Mathematics (Held on 18th Feb 2019) Official Paper
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  1. 1
  2. −1
  3. 0
  4. Does not exist.

Answer (Detailed Solution Below)

Option 4 : Does not exist.
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RPSC Senior Grade II (Paper I): Full Test 1
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Detailed Solution

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Concept Used:

Definition of modulus function:

\(|x|=\begin{cases}x,& x\geq0\\ -x,& x<0\end{cases}\)

Calculation:

\(|x-2|=\begin{cases}x-2,& x-2\geq0\\ -x+2,& x-2<0\end{cases}\)

⇒ \(|x-2|=\begin{cases}x-2,& x\geq2\\ -x+2,& x<2\end{cases}\)

f'(2+) = 1 (LHD)

f'(2-) = -1 {RHD)

LHD ≠ RHD 

Hence, f'(2) doesn't exist.

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