document.write( "Question 1142707: Calculus Optimization Question\r
\n" ); document.write( "\n" ); document.write( "A rectangular garden is to be surrounded by a low fence. There is only 100 feet of fencing available for all four sides. What is the largest possible area of the garden that can be fenced? \n" ); document.write( "

Algebra.Com's Answer #763434 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "If x is the length of the garden, then its width is   feet, and the area is\r\n" );
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document.write( "    A(x) =  = \r\n" );
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document.write( "They want you find the maximum of the function A(x) using Calculus.\r\n" );
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document.write( "For it, differentiate A(x) over x and equate the derivative to zero:\r\n" );
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document.write( "    A'(x) = -2x + 50 = 0,\r\n" );
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document.write( "which gives you  x =  = 25 feet.\r\n" );
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document.write( "Thus you obtain the\r\n" );
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document.write( "ANSWER.  Under given conditions, the maximum area is achieved for the square of the side length equal to \r\n" );
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document.write( "         one fourth of the given perimeter, i.e.  25 feet.\r\n" );
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\n" ); document.write( "\n" ); document.write( "This result is VERY WELL known and can be obtained by means of Algebra, too.\r
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\n" ); document.write( "\n" ); document.write( "See the lessons\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "    - A rectangle with a given perimeter which has the maximal area is a square\r
\n" ); document.write( "\n" ); document.write( "    - A farmer planning to fence a rectangular garden to enclose the maximal area\r
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