there is a function which is differentiable continuously on [a,b] .
suppose
|f'(x)|<1
for all
prove that there exists
0<=k<1
that this equation is true
i got a solution to this..but i cant understand it.
they make mean value theorem on f'(x) [x1,x2] so x2>=x1
then they say that by the second law of weirsstas there is a minimum and maximum
so there is l,L on [a,b] so
f'(L)>=f'(x)>=f'(l) for every x in [a,b]
i cant understand what is the second law of weirshtass
that gives two extreme points??
there is another things but i got stuck on this
??