Question

Find the derivatives from the left and from the right at x=1 (if they exist). Is the function differentiable at x=1?

f(x)=|x-1|

Please help! I have no idea how to find the derivative from the left and right..

Answer 1

Look at when "x" approaches from the left here |x-1|<=1
and when "x" approaches from the right here |x-1|>=1

In order for it to be differential it has to be:
1-Continuous
2-Not have any sharp turns

Answer 2

Slight correction on the first post; the left- and right- derivatives are the one-sided limits of the derivative of \(f\), not \(f\) itself.

You can conclude that \(f\) is differentiable at 1 if \(\lim_{x\to1^-}f'(x)=\lim_{x\to1^+}f'(x)\).

Answer 3

Oh shoot I forgot the derivitive. My bad

Answer 4

Thanks for correcting me