EXAMPLES OF MAXIMA AND MINIMA." 211? 



1 . Shew that x 5 5x* + 5x 8 1 is a maximum when x=l; 

 a minimum when x = 3 ; neither when x 0. 



2. Shew that x 3 3a? -f 3x + 7 is neither <a maximuni nor 



a minimum when x= 1. 



3. If u = x 3 3ce 2 + Gx + 7, shew that it has neither a 



maximum nor a minimum value. 



4. . If u = x 3 9a; 2 + 15x 3, find its maximum and mini- 



mum value. 



A maximum when x = 1 ; a minimum when x = 5. 



A maximum when x = fy\ a minimum when x = 1 ; 

 neither when x = 2 t 



6. u= 



A maximum when oj = 1 ; a minimum when x = 0, 

 and when x = 7. 



7. w = 3z 6 - 125ic 3 + 216(ke. 



. A maximum when x = 4, and when x = 3 ; 

 a minimum when a? = 3, and when x = 4. 



1 :r + a; 2 



8. w = - - . A minimum when x ="|. 



1 + a; ic 2 



a; 2 - 7# + 6 



9. w = - . 



# 10 



A maximum when x = 4 j a minimum when a; = 16. 



10. If ^ = x* (x - I) 2 (x - 2) 3 (a; - 3) 4 , find when u is a 



maximum or minimum. 



A maximum when x = ; a minimum when x = 2. 



(Lilt ' 



11. If -r- = (a; 1) (a? 2) 2 (a; 3)*, find when w is a maxi- 



CLCC 



mum or minimum, 



A maximum when x = 1 j a minimum when x = 3. 



P2 



