( 25.^ ) 



We liavc therefore : 



dT RT'.r 1 inWv 1 



when ji' is great with respect to 6, and iicjice : 



, dx f dx\ 



Consequently this is 0, when 



, dx f d.r\ 



dx \ dx J 



dx 

 Now Ave nia\- write for — (see (/>) ) : 



dx 

 dx _x{l—x) 1 



d^' ~ i/ r^i^- 



80 that — — = 0, when 

 dx ^ 



.r(l — :r)z=,r\ 1 — [1 x — 



1-^x ƒ 



or 



1— .r 

 l—x= l-^'xl 1 + 



1-^'x/ 

 or 



i—^ixj y 1 -,i'./ 



From this \\g tind : 



1 r - Ï'' T 



SO finally : 



'^^ = ^' (12) 



being the value of .c, at which for large Aalues of li' the point of 



inflection will be situated after the niaxiniuni at ,r =: — (see (11)). 



So this \'alue of ,r too approaches to 0, when ,i' approaches to oc. 



It is now evident that according to (10) for large values of /?' the 



A/-7'\ 

 quantity -7^ approaches to — x. For alreadv ui the biniiedlate 



neighbourhootl of A the direction of the curve 7'= /'(■/•'), Avhich was 

 initially almost vertical, changes into a [lerfectly vertical direction at 

 the maximum. 



