Help with analisys question

[Beren1936]

Suppose that f : [0; 1] -> R is a continous function.

A. Show that the function F: [0; 1] -> R defined by is differentiable in (0; 1), and that for all x E (0; 1) worth F' (x) = f (x);

B. Suppose that f: [0; 1] -> R is additionally differentiable at (0; 1). If for each x E [0; 1] worth the relationship
and f (x) =/= 0 for all x E (0; 1), deduce that f (x) = x for all x E [0; 1].

C. If f> 0, show that

 

[Steven G]

These are great questions. It is unfortunate that you do not want to be involved with discussion these problems.

Just for the record this is not a drop off your homework problems and come back later for the solutions type of website. It is a math help forum.

 

[Beren1936]

I actually solved item A through the theorem shown in Rudin's book, but on B, i don't know how start

 

[tkhunny]

Have you considered showing your work, rather than making us guess?

I suspect you start Part B by successfully completing Part A.

 

[Beren1936]

here