The page looks good to me. Well done!

Bob

]]>May I use some of your wording Nehushtan?

I certainly would, JFF could not have said it better.

In post #2 I left out the other part of the function definition. I should have said,

f(x) is differentiable at 0 according to the SE. x^2 sin( 1/ x ) would not be because it is not defined at 0.

]]>May I use some of your wording Nehushtan?

]]>The Floor and Ceiling Functions are not differentiable, as there is a discontinuity at each jump.

More precisely, they are not differentiable only at integer values of *x*. (If *x* is not an integer they are perfectly differentiable at *x*.)

Similarly the function so *y*=*x*[sup](1/3)[/sup] is only not differentiable at the origin; elsewhere it is differentiable.

The *y*=1/*x* and *y*=sin(1/*x*) are not defined at the origin so it makes no sense to ask whether they are differentiable there. To be differentiable at a certain point, the function must first of all be defined there!

And the last part:

But a c̶o̶n̶t̶i̶n̶u̶o̶u̶s̶ ̶f̶u̶n̶c̶t̶i̶o̶n̶

function that is continuous at a certain pointmight not be differentiableat that point, for example the absolute value function is actually continuous (though not differentiable)at the origin.

Looks good!

Interesting is that the function sin( 1 / x ) is not differentiable at 0 and neither is x sin( 1 / x ) but x^2 sin( 1 / x ) is!

]]>Is it correct?

Ideas for improvement?

]]>