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  • Find two numbers whose sum is 24 and whose product is as large as possible.

14. Find two numbers whose sum is 24 and whose product is as large as possible.

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Let x and y are two numbers
It is given that
x + y = 24 , y = 24 - x
and product of xy is maximum 
let f(x) = xy=x(24-x)=24x-x^2\\ f^{'}(x) = 24-2x\\ f^{'}(x)=0\\ 24-2x=0\\ x=12
Hence,  x = 12 is the  only critical value
Now,
f^{''}(x) = -2< 0
at x= 12  f^{''}(x) < 0
Hence, x = 12 is the point of maxima
Noe, y = 24 - x
            = 24 - 12 = 12
Hence, the value of x and y are 12 and 12 respectively
 

Posted by

Gautam harsolia

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