Is the absolute value of x -1 differentiable at x?

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01-07-2018
Mathematics

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Is the absolute value of x -1 differentiable at x?

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DeanR DeanR · Answer 1 · 2018-07-01T13:15:32+02:00

DeanR DeanR

01-07-2018

[tex]f(x)=|x-1|[/tex]

is differentiable everywhere except at [tex]x=1.[/tex] There the derivative limit from the left gives -1 and from the right +1, different, so no derivative at [tex]x=1.[/tex]

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