document.write( "Question 1135313: Please answer this optimization problems
\n" ); document.write( "1:find the number/s in the interval I=[1/2,3] such that the sum of the number and it's reciprocal is a minimum.
\n" ); document.write( "2:A wire measuring 12 ft long is cut into pieces. One piece is to be bent into a square and the other into a circle. How should the wire be cut so that the combined area is as large as possible?
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Algebra.Com's Answer #752960 by ikleyn(52798) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "1.  They ask you to find the minimum of the function\r\n" );
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document.write( "        f(x) = x + \r\n" );
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document.write( "    in the interval  I = [1/2, 3].\r\n" );
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document.write( "    Take the derivative, equate it to zero and find the root:\r\n" );
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document.write( "    f'(x) = 1 - ;   f'(x) = 0  is the equation  1 -  = 0;\r\n" );
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document.write( "    as an equation, it is equivalent to   = 1,  which has only one root  x= 1  in the given interval.\r\n" );
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document.write( "    ANSWER.  x = 1.\r\n" );
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document.write( "To better illustrate the situation for you, I placed the plot below:\r\n" );
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document.write( "    \r\n" );
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document.write( "        Plot y = x + .\r\n" );
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