document.write( "Question 1024797: Find the absolute extrema of
\n" ); document.write( "f(x)=x^a(1-x)^b
\n" ); document.write( "where 01\r
\n" ); document.write( "\n" ); document.write( "I have the derivative
\n" ); document.write( "f'(x)=ax^(a-1)(1-x)^b-x^(a)b(1-x)^(b-1)\r
\n" ); document.write( "\n" ); document.write( "Unsure of where to go from this point. Thank you for the help \n" ); document.write( "

Algebra.Com's Answer #640156 by ikleyn(53765) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Find the absolute extrema of
\n" ); document.write( "f(x)=x^a(1-x)^b
\n" ); document.write( "where 01\r
\n" ); document.write( "\n" ); document.write( "I have the derivative
\n" ); document.write( "f'(x)=ax^(a-1)(1-x)^b-x^(a)b(1-x)^(b-1)\r
\n" ); document.write( "\n" ); document.write( "Unsure of where to go from this point. Thank you for the help
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
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\n" ); document.write( "\n" ); document.write( "

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document.write( "Next step is to write an equation f'(x) = 0, which gives you this:\r\n" );
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document.write( " = .   (1)\r\n" );
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document.write( "Now cancel both sides of (1) by the factor . You will get\r\n" );
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document.write( "a*(1-x) = b*x.\r\n" );
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document.write( "a - ax = bx\r\n" );
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document.write( "a = (a+b)*x,\r\n" );
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document.write( "x = .   1-x = .\r\n" );
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document.write( "f(x) = .\r\n" );
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