Question

Please explain:
Prove that the derivative does not exist at the given value.
f(x)=|x-3| , x=3
(we have to use the alternative definition of the derivative to show that they have two different slopes coming from the left and the right. but i dont know how to show it!

Answer 1

do the followings: 1. find the derivative of the left slope with 3-.
2. find the derivative of the right slope with 3+.
then 1 and 2 should not be equal at x=3 since f(x) is a function of absolute of x-3.

Answer 2

Hi! Thanks for the answer! really appreciate it. but how do you find the derivatives of the absolute value? my teacher did it as f'(x) approaching from left = lim x->-3 |x-3|/x-3 and the same thing except from the right and he miraculously got the slope of -1 and 1. I don't know how he arrived to that. Sorry for confusing wording.