document.write( "Question 1040516: Solve the following optimization problem: Minimize x^3-10x^2+6
\n" ); document.write( "Then I must determine whether the solutions are locally or globally optimal
\n" ); document.write( "Thank you,
\n" ); document.write( "June \n" ); document.write( "

Algebra.Com's Answer #655322 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"y+=+x%5E3+-10x%5E2+%2B+6\"$ ==> y' = $\"3x%5E2+-+20x\"$ ==> y\" = 6x - 20.\r
\n" ); document.write( "\n" ); document.write( "Setting y' = 0 gives x = 0, 20/3.\r
\n" ); document.write( "\n" ); document.write( "At x = 0, y\" = -20 < 0, ==> local maximum by the 2nd derivative test. (Not global, since $\"lim%28x-%3Einfinity%2Cy%29+=+infinity\"$ .)\r
\n" ); document.write( "\n" ); document.write( "At x = 20/3, y\" = 20 > 0, ==> local minimum by the 2nd derivative test. (Not global, since $\"lim%28x-%3E-infinity%2C+y%29+=+-infinity\"$ .) \n" ); document.write( "

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