document.write( "Question 143035: question is to prove that the function f(x)=|x-1|,xeR is not differentiable
\n" ); document.write( "at x=1? \n" ); document.write( "

Algebra.Com's Answer #104094 by nabla(475) $\"\"$ $\"About$

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Prove that f(x) = |x-1| is not differentiable at (1,0).
\n" ); document.write( "Proof: y=f(x) = |x-1|
\n" ); document.write( "We use a direct proof.
\n" ); document.write( " $\"%28%28delta%29y%29%2F%28%28delta%29x%29=%28%28delta%29f%29%2F%28%28delta%29+x%29\"$ =y'= $\"lim%28+h-%3E0%2C%28%28abs%28x-1%29%2Bh%29-abs%28x-1%29%29%2Fh%29\"$ (first principle)
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(rationalization)
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\n" ); document.write( "= $\"lim%28+h-%3E0%2C%28-2%2Bh%2B2x%29%2F%28%28abs%28x-1%29%2Bh%29%2Babs%28x-1%29%29%29\"$
\n" ); document.write( "= $\"%282x-2%29%2F2abs%28x-1%29\"$ = $\"%28x-1%29%2Fabs%28x-1%29\"$
\n" ); document.write( "When x=1,y'=0/0 which is undefined.
\n" ); document.write( "f(x) = |x-1| is not differentiable at x=1.\r
\n" ); document.write( "\n" ); document.write( "Q.E.D. \n" ); document.write( "

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