Question
Download Solution PDFIf f(x) = |x − 2|, then f'(2) equals :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept 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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