# Show the absolute value of a function is not differentiable?

Show y=|x-2| is not differentiable at x=2, by showing that the limit in the definition of the derivative does not exist

### 2 Answers

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- PinkgreenLv 75 months ago
y=|x-2|=x-2, when x>2

y=|x-2|=0, when x=2

y=|x-2|=-x+2, when x<2

Consider

limit [(2-2+h)-(2-2)]/h=1

h->0+

limit [-(2+h-2)-(-2+2)]/h=-1

h->0-

Since the limits are not equal,

the derivative of y at x=2 does

not exist.

- AmyLv 75 months ago
The problem tells you what to do.

Start with the definition of a derivative. Fill in y = |x-2| and x=2.

After you cancel out all the 2's, you're left with a fairly simple limit statement. Try to evaluate that limit from both directions.

Why does the limit not exist?

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