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Question Number 214342 by issac last updated on 06/Dec/24

why

differantiable f \to f is continious

but f is continous ↛ differantiable ? ?

Commented by mr W last updated on 06/Dec/24

a s m o o t h l i n e i s a l w a y s c o n t i n o u s,

b u t a c o n t i n o u s l i n e i s n o t a l w a y s

s m o o t h .

Commented by mr W last updated on 06/Dec/24

Commented by mr W last updated on 06/Dec/24

a l l a r e c o n t i n i o u s, b u t n o t a l l a r e

s m o o t h (d i f f e r e n t i a b l e) .

Answered by Frix last updated on 06/Dec/24

Just think of an example :

f (x) =∣ x ∣ is continuous but not differentiable

at x = 0

g (x) = \sqrt[3]{x^{2} - 1} is continuous but not differentiable

at x = \pm 1

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