

F 



g. 3, e-nx 



Fig. 3, e+nx 



oim 



No. 





No. Value of n 





15 





15 +0 



J 



16 



h 



22 1 



| 



17 



h 



23 I 



1 18 







2 19 



2 



25 2 



3 



20 



3 



26 3 



In Fig. 4, the curves are £ 



No. Value of p ' No. 



Fig. 4a shews more clearly t 

 oo, a' being positive throughou 



(ii) Curve 

 (iii) Curve 



3. Points of inflection of constituent 

 derivative of v m is d 2 ifjd .r 2 = m (m — 1) 

 of inflexion can exist only if . 

 changes. 



The second derivative of the curve y 

 d 2 y/dx- = e DxV {{npx v ^) 2 + np{p- 

 so that putting this equal to zero, the 

 are given by 



■The second 

 ) <r m - 2 ; hence a point 

 sign of the derivative 



The conditions for points of inflexion, see Figs. I, ia and 

 b are complex and may be stated as follows : — 



