document.write( "Question 1027080: What is the smallest possible value of 2x^4 + 8/x^4 over all real nonzero values of x? \n" ); document.write( "

Algebra.Com's Answer #642348 by Fombitz(32388) $\"\"$ $\"About$

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Use the derivative,
\n" ); document.write( " $\"f%28x%29=2x%5E4%2B8x%5E%28-4%29\"$
\n" ); document.write( " $\"df%2Fdx=8x%5E3-32x%5E%28-5%29\"$
\n" ); document.write( "Set it equal to zero,
\n" ); document.write( " $\"8x%5E3-32x%5E%28-5%29=0\"$
\n" ); document.write( " $\"%288x%5E8-32%29%2Fx%5E5=0\"$
\n" ); document.write( " $\"8x%5E8=32\"$
\n" ); document.write( " $\"x%5E8=1%2F4\"$
\n" ); document.write( " $\"x=0+%2B-+%284%29%5E%281%2F8%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=0+%2B-+%282%29%5E%281%2F4%29\"$
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\n" ); document.write( "So then,
\n" ); document.write( " $\"f%5Bmax%5D=2%2A%282%5E%281%2F4%29%29%5E4%2B8%2F%28%282%5E%281%2F4%29%29%5E4%29\"$
\n" ); document.write( " $\"f%5Bmax%5D=2%2A2%2B8%2F2\"$
\n" ); document.write( " $\"f%5Bmax%5D=4%2B4\"$
\n" ); document.write( " $\"f%5Bmax%5D=8\"$ \r
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