document.write( "Question 962755: Find two numbers whose difference is 60 and whose product is as small as possible. [hint: let x and x-60 be the two numbers. their product can be described by the function f(x)=x(x-60).] \n" ); document.write( "

Algebra.Com's Answer #588212 by hkwu(60) $\"\"$ $\"About$

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Just minimize the function. Calculating f'(x), we get
\n" ); document.write( " $\"d%2F%28dx%29%2Af%28x%29=2x-60\"$
\n" ); document.write( "since
\n" ); document.write( " $\"f%28x%29=x%5E2-60x\"$
\n" ); document.write( "Setting it to 0, we get
\n" ); document.write( " $\"2x-60=0\"$
\n" ); document.write( " $\"2x=60\"$
\n" ); document.write( " $\"x=30\"$
\n" ); document.write( "You can do the first derivative test to make sure it is actually a minimum point. If x = 30, then
\n" ); document.write( "x - 60 = -30
\n" ); document.write( "and thus the two numbers are 30, -30.
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\n" ); document.write( "Leave a message if I helped. \n" ); document.write( "

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