If is continuous on and differentiable at a point , show that, for some pair ,

whenever

Since it's differentiable at x I know exists...

And it's continuous so I know for that for any there's a so that when

Not sure how to put it all together...

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- May 19th 2009, 06:40 AMMMath09Differentiable, continuous function... "show that"
If is continuous on and differentiable at a point , show that, for some pair ,

whenever

Since it's differentiable at x I know exists...

And it's continuous so I know for that for any there's a so that when

Not sure how to put it all together... - May 19th 2009, 07:29 AMHallsofIvy
Try using the mean value theorem instead.

- May 19th 2009, 08:21 PMMMath09
- May 20th 2009, 01:55 PMHallsofIvy
Oops, right, I didn't see that! Sorry. I guess you were right to use the definition of "differentiable at a point".

Let n be any integer strictly larger than f'(x)+1. Certainly there exist [itex]\delta> 0[/itex] such that And, since is a real number, there exist [tex]m> \frac{1}{\delta}[/itex]. If then |\frac{f(t)- f(x)}{x-t}|< n. - May 21st 2009, 04:01 AMMMath09