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If f ( x ) = |x - 3|, then f' ( 3...

If ` f ( x ) = |x - 3|`, then ` f' ( 3 ) ` is

A

` - 1 `

B

` 1`

C

0

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
D
Given, ` f ( x ) = |x - 3| `
Redefine this function ,
` f ( x ) = {{:( 3 - x ",", x lt 3 ) ,( 0" "",", x = 3 ) ,( x - 3",", x gt 3 ) :} `
` f' ( x ) = {{:( - 1",", x lt 3 ),( 0",", x = 3 ) , ( 1",", x gt 3 ):} `
It is clear that, ` Lf ' ( 3 ) ne Rf' ( 3 ) `.
` therefore f' (3 ) ` does not exist.
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