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
- PinkgreenLv 76 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
Since the limits are not equal,
the derivative of y at x=2 does
- AmyLv 76 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?