suppose-that-f-0-1-R-lets-f-C-2-and-suppose-that-0-1-such-that-f-f-1-1-proof-or-give-a-counter-example-that-0-1-f-

Question Number 2289 by 123456 last updated on 14/Nov/15

suppose that f : [0, 1] \to R, lets f \in C^{2}

and suppose that \exists α \in [0, 1] such that

f (α) + f (1 - α) = 1

proof or give a counter example that

\exists ξ \in [0, 1], f (ξ) = ξ

Commented by Rasheed Soomro last updated on 15/Nov/15

{THANK}^{S}! {I t}^{'} s i n c r e a s e i n m y k n o w l e d g e .

Commented by RasheedAhmad last updated on 15/Nov/15

I f f : [0, 1] \to R m e a n s x \in [0, 1] a n d f \in R

t h e n w h a t i s t h e m e a n i n g o f

f \in C^{2} ?

Commented by prakash jain last updated on 15/Nov/15

f \in C^{0} continuous function

f \in C^{1} differentiable function and derivative

is continous

f \in C^{2} double differentiable and second derivative

is continous .

similarly

f \in C^{k} or f \in C^{\infty}