If is differentiable with and and is continuous with as then prove that f is differentiable at 0.

So, from the definition we want to show that exists.

From we have

Then,

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- May 21st 2011, 04:33 AMcanaDifferentiability definition
If is differentiable with and and is continuous with as then prove that f is differentiable at 0.

So, from the definition we want to show that exists.

From we have

Then,

- May 21st 2011, 07:02 AMHallsofIvy
If you are asking if that is a valid proof, yes, it is. Very well done! The one comment I would make is that the middle term in

is not necessay. Just set f(0) in equal to 0 to go directly: