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...
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...
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.