show that f(x) = ∣x∣ is not differentiable at x=0, where ∣x∣ denotes he absolute value function


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Question Number 73566 by Rio Michael last updated on 13/Nov/19

$s h o w t h a t f (x) = ∣ x ∣ i s n o t d i f f e r e n t i a b l e a t x = 0, w h e r e ∣ x ∣$ $d e n o t e s h e a b s o l u t e v a l u e f u n c t i o n$
Commented by Rio Michael last updated on 13/Nov/19

$t h a n k s s i r,$ $b u t w h e n l o o k i n g a t d i f f e r e n t i a b i l i t y$ $s h o u l d w e t a k e$ $d e r i v a t i v e s a t x = 0 f r o m b o t h d i r e c t i o n ?$
Commented by kaivan.ahmadi last updated on 13/Nov/19

$f_{-}^{'} (0) = - 1$ $f_{+}^{'} (0) = 1$
Commented by malwaan last updated on 14/Nov/19

$y e s$
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