Determine if the following function f is differentiable at point indicated. If it not differentiable, explain

f(x) = { sin (1/x) if x not equal to 0
{ 0 if x = 0

It's not because the function is NOT CONTINUOUS near x=0.

Think of it this way, would you have to pick up your pencil drawing this function? YES! There is no way to continuously draw the function from x=0 to other x values without picking up your pencil.

Hope that helps