318 POINTS OF INFLEXION. EXAMPLES. 



3. If y (a 4 Z> 4 ) = x (x a) 4 xb*, there is a point of inflexion 



2a 

 when x = . Is there a point of inflexion when 



a; = a? 



?/ //<2 ~ X\ 



4. If - = *l I - j , there is a point of inflexion when 



3a 

 V--. 



5. If - = + ( ) there is a point of inflexion when 



a a \ a J 



6. If or = log y, there is a point of inflexion when x = 8. 



7. If ax* x y y c?y = 0, there is a point of inflexion when 



8. If - = A/(V- ~)> th ere i s a Pi nt f inflexion when 



a 



-r 



flS 



9. 1i xy = a* log - , there is a point of inflexion when 



# = ae^. 

 10. Find the point of inflexion on the curve, 



{y - 2 4/(a 2 tf)} 2 = lax. Result, x = a. 



11. If T/ (a; 2 + a 2 ) = a 2 (a a*), there are three points of in- 



flexion which lie on a straight line. 



12. If r = ~f , there is a point of inflexion when r~. 



v 1 *> 



13. If r = b . 6*, there is a point of inflexion when 



14. If a; = a(l cos<), and y = a (n$ + sin 0), there is a 

 point of inflexion when cos < = . 



