Need some help in showing that the function f '(x) is not continuous at 0.
Here is the problem: Consider the function f(x) defined by
f(x)= x2sin(1/x) if x does not = 0
0 if x = 0
Show that the function f ' (x) is not continuous at 0.
Any help would be appreciated.
Re: Need some help in showing that the function f '(x) is not continuous at 0.
Quote:
Originally Posted by
marsalanuddin 
Here is the problem: Consider the function f(x) defined by
f(x)= x2sin(1/x) if x does not = 0
0 if x = 0
Show that the function f ' (x) is not continuous at 0.
Any help would be appreciated.
Use the limit definition of the derivative and the squeeze theorem to prove that )
is differentiable. Then just use the product and chain rule to find the derivative. Once you have )
show that  \ne f'(0))
Hint the limit of the derivative does not exist
