Show that f(x)=|x−5| is continuous but not differentiable at x=5

Minawiukd

Minawiukd

Answered question

2023-02-04

Show that f(x)=|x−5| is continuous but not differentiable at x=5

Answer & Explanation

rocairasen

rocairasen

Beginner2023-02-05Added 7 answers

For continuity at x=5 , L H L = lim x 5 ( x + 5 ) = lim h 0 [ ( 5 h ) + 5 ] = lim h 0 h = 0 R H L = lim x 5 + ( x 5 ) = lim h 0 ( 5 + h 5 ) = lim h 0 h = 0 f ( 5 ) = 5 5 = 0 L H L = R H L = f ( 5 ) f(x) is continuous at x=5 L f ( 5 ) = lim x 5 f ( x ) f ( 5 ) x 5 = lim x 5 x + 5 0 x 5 = 1 R f ( 5 ) = lim x 5 + f ( x ) f ( 5 ) x 5 = lim x 5 + x 5 0 x 5 = 1 L f ( 5 ) R f ( 5 ) f(x)=|x-5| is not differentiable at x=5

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