Examples And Solutions of the Differential Calculus

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x + a ITS?
\\Tience x = y= \~j- Therefore the altitude must be made equal to the radius of the base.
TWO OR MORE VARIABLES. 77 (10. ) u=a? t 2>axy+y i find the values of x and y which render u a maximum or minimum.
x=a ) yCL, u=& minimum when a is positive, and a maximum when a is negative.
(11. ) u = aa? Ijx^y -f y 1, find the values of x and y which make u a maximum or minimum.
(12. ) u=aa?y 2 x^y 1 x^y^ ; find the values of x and y which make u a maximum or minimum. A a maximum. 2 (13. ) u=(
...l- ^ - -) (l- ^) ; find the values of x * y> and y which render u a maximum or minimum.
7T (14. ) u=a cos 2 #-f-& cos 2 y, where y=--r -\-x\ find the values 4 of cos# and cosy which make u a maximum or minimum.
! + - rf =1 * 2 ~~ 2 \/ 2 4- 6 2 2 2 ), a maximum with the upper, and a minimum with the lower sign.
(15. ) Divide a given number a into three such parts #, y, and #, that -^--\ -\ shall be a maximum or minimum, J o 4 and determine which it is.
(16. ) Inscribe the greatest triangle within a given circle.


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