SOLUTION: question is to prove that the function f(x)=|x-1|,xeR is not differentiable at x=1?

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Question 143035: question is to prove that the function f(x)=|x-1|,xeR is not differentiable
at x=1?
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
Prove that f(x) = |x-1| is not differentiable at (1,0).
Proof: y=f(x) = |x-1|
We use a direct proof.
%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)
= (rationalization)
=
=
=lim%28+h-%3E0%2C%28-2%2Bh%2B2x%29%2F%28%28abs%28x-1%29%2Bh%29%2Babs%28x-1%29%29%29
=%282x-2%29%2F2abs%28x-1%29=%28x-1%29%2Fabs%28x-1%29
When x=1,y'=0/0 which is undefined.
f(x) = |x-1| is not differentiable at x=1.
Q.E.D.