what is the difference between continuity and differentiability?

Asked by manojmathematics11 | 4th Jun, 2015, 04:34: AM

Expert Answer:

C o n t i n u i t y space d e f i n e s space w h e t h e r space a space f u n c t i o n space i s space c o n t i n o u s space o r space n o t. D i f f e r e n t i a b i l i t y space d e f i n e s space w h e t h e r space a space f u n c t i o n space i s space d i f f e r e n t i a b l e space o r space n o t.  E v e r y space d i f f e r e n t i a b l e space f u n c t i o n space i s space c o n t i n o u s comma space w h e r e a s space e v e r y space c o n t i n o u s space f u n c t i o n space m a y space n o t space b e space d i f f e r e n t i a b l e. L i t e r a l l y space s p e a k i n g comma space w e space c a n space s a y space t h a t space i f space a space f u n c t i o n space h a s space a space s h a r p space e d g e space a n d space n o space b r e a k space i n space t h e space g r a p h comma space i t space i s space a space c o n t i n o u s b u t space a space n o n minus d i f f e r e n t i a b l e space f u n c t i o n.  F o r space e x a m p l e comma t h e space g r a p h space o f space y equals vertical line x vertical line space i s space a space c o n t i n o u s space f u n c t i o n space b u t space i s space n o t space d i f f e r e n t i a b l e.

Answered by Prasenjit Paul | 4th Jun, 2015, 09:35: AM