Question

Show that the absolute value function f(x) = lxl is not differentiable at x =0

Answer 1

because you can't take the derivative at x=0 because it is a corner

Answer 2

lim f( 0+h) - f(o) / h

how to show it using this?

Answer 3

I think you need to use a not h
and don't forget (as x approaches 0) notation
Show that the right hand limit does not equal the left hand limit

Answer 4

so if left hand doesnt equal right hand, that means it is not differentiable?

Answer 5

if the left hand limit does not equal the right hand limit, the limit does not exist.
show that the derivative of the left hand limit does not equal the derivative of the right hand limit, the derivative does not exist.
If the derivative does not exist then it is not differentiable
use a piecewise function to describe the absolute value function

Answer 6

oh ok i get it now thanks