document.write( "Question 427186: determine the local minimum and maximum values of f(x)=(3x^2-6x)(3x^2+6x), to the nearest hundredth.
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Algebra.Com's Answer #297135 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"y+=+%283x%5E2-6x%29%283x%5E2%2B6x%29+=+9x%5E4+-+36x%5E2\"$
\n" ); document.write( "==> $\"dy%2Fdx+=+36x%5E3+-+72x\"$
\n" ); document.write( "Let this equal 0:
\n" ); document.write( " $\"36x%5E3+-+72x+=+36x%28x%5E2+-+2%29+=+0\"$ ==> x = 0, $\"sqrt%282%29\"$ , $\"+-sqrt%282%29\"$ .
\n" ); document.write( "Also, $\"d%5E2y%2Fdx%5E2+=+108x%5E2+-+72+=+36%283x%5E2+-+2%29\"$
\n" ); document.write( "When x = 0, $\"d%5E2y%2Fdx%5E2+%3C+0\"$ ==> local max there, and so local max value is y = 0.
\n" ); document.write( "When x = $\"sqrt%282%29\"$ or $\"-sqrt%282%29\"$ , $\"d%5E2y%2Fdx%5E2+%3E+0\"$ , ==> local mins there, and so local (absolute) min value is y = -36.
\n" ); document.write( "(There is no absolute max value.)\r
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