Question

f(x) = I x-2 I ( Absolute value of x-2)

Use the defination of the derivative to show that
f'(2) does not exist.

Answer 1

That means using the first principle :)

Try evaluating the value of \(\huge\lim\limits_{h\rightarrow0}\frac{|x+h-2|-|x-2|}h\)

Answer 2

Hint: Seperate it into cases?

Answer 3

you'll find that some cases lead to 1 while some lead to -1.

Answer 4

oh yeh, I did that, I differentiated using 1st principles -x+2, and also x-2. I got the values of -1 and 1 respectively. So, because they are not the same, can I therefore conclude that it does not exist?

Answer 5

yep :)

Answer 6

thanx a million kc.

Answer 7

no problem at all :D