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The product of two numbers is 192. Find the numbers when the sum of the first and three times the
second is a maximum.

 Jan 29, 2021
 #1
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Let the first be  x  and the second be   192 /x

 

And we wish to maximize

 

x+  (3 )  ( 192/x)

 

x +  576x^(-1)         take the derivative and set to 0

 

1  - 576x^-2   = 0

 

1   576 / x^2

 

x^2  =576

 

x  = 24   or x   =  -24

 

The second derivative is    2*576/ x^3         this will  be negative when x   = -24   so  this is a (relative)  max

 

So   the  numbers  are   -24   and   192/-24  =   -8

 

 

cool cool cool

 Jan 29, 2021

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