corolari del valor mitx

Si ( f(0) = 0 & f(1) = 0 & d_{x}[f(x)] és creishent ==> ...
... [∀x][ x€(0,1)_{K} ==> ( f(x)/x ) és creishent ]


sigui 0 < x [< y < 1 ==>
[∃c][ 0 [< c [< x ] & [∃b][ y [< b [< 1 ]
(f(x)/x) = ( (f(x)+(-1)f(0))/(x+(-0)) ) = d_{x}[f(c)] [< d_{x}[f(x)] [< ...
... d_{y}[f(y)] [< d_{y}[f(b)] = ( (f(1)+(-1)f(y))/(1+(-y)) ) [< ( f(y)/y )
0 [< 1
(-y) [< 1+(-y)


f(x) =  x·(x+(-1))
d_{x}[f(x)] = 2x+(-1)


(f(x)/x) =  x+(-1)