212 EXAMPLES OF MAXIMA AND MINIMA. 



12. w = (<*+)'(-*)* 



A maximum when x = - , and when x = a, 



o 



and a minimum when x = - , 



t 



A minimum when x = r . 



14. u = b + c(x- a). 



A minimum when x = a. 



a 

 lo. u= 



x a x 



A minimum when x = r and a maximum when 



a + b 



a* 

 X ~a-b' 



16. -== 



( 



A minimum when x 0, and a maximum when x=a. 



17. u = (mx + na) m+n (m + n) m+n x m a*. 



A minimum when x = a. 



OR 



18. Shew that is a maximum when x = cos x. 



1+x tan x 



19. Shew that x* is a maximum when # = e. 



20. Shew that x is a maximum when x = - . 



tan 3x 8 



7T 



21. Shew that sin x (1 + cos x} is a maximum when x = . 



9 



22. If xy(y x)= 2a 8 , shew that y has a minimum value 



when x = a. 



