EXAMPLES OF MAXIMA AND MINIMA. 213 



23. If Scfy* + xy* + lax 3 = 0, shew that when x = , y has 



2 



d a v 

 a maximum value, namely 3a, the value of -5-^ being 



then - . 

 5a 



24. If a;* + 2ax*y ay 3 = 0, shew that when x = a, y =* a 



and is a minimum. Also, when y = , a; is both 

 y 



j . . 4aV6 , 



a maximum and minimum, and is = + ~ . 



y 



25. If 2# 5 + Say* o;*y = 0, shew that x = a . 5 s makes y a 



minimum, and = a . 5 U . 



26. Find the maximum and minimum value of y, when 



y* 4c 3 yx + a? = 0. 

 x c \/3 makes y = c ^(27) a maximum. 



a; = c ^3 makes y = c ^(27) a minimum. 



i 



27. A person being in a boat 3 miles from the neatest point 



of the beach, wishes to reach in the shortest time a 

 place 5 miles from that point along the shore : sup- 

 posing he can walk 5 miles an hour, but row only at 

 the rate of 4 miles an hour, required the place where 

 lie must land. 



One mile from the place to \>e reached. 



28. The sides of a rectangle are a, and b : shew that the 



greatest rectangle that can be drawn so as to have its 

 sides passing through the corners -of the gi^ven rect- 

 angle is a square, each side of which is - . 



V 2 O 



29. If a rectangular piece of pasteboard, the sides of which 



are a and b, have a square cut out at each ^qrner, find 

 the side of the square that the remainder may form a 

 box of maximum content. r 



rru -J a + b-*j'(a*- 

 .The side = - 



