continuity and differentiability
Hello I would just like you to tell me what would be the best method to demonstrate that the function g is of class on the interval J(I was spoken to apply Taylor Lagrange or Taylor-Young but I did not understand much) I thank:
Here is the statement:
Let f be a function of class over an interval J, such that f (0) = 0.
It is assumed that 0 is an interior point to J. We define the function g on J by:
and g (0) = f '(0).
What I have done yet below:
In a first time I apply Taylor Young to see where that leads me
-The formula for Taylor Young in 0 to order 2 of f gives us
or f (0) = 0 therefore
I wonder now if this is fair and whether it will indeed serve me something.
(I just want to say that I'm French and I think you'll find my language can be a little too basic, I hope that this will not prevent you from answering me)