document.write( "Question 1086873: Find the absolute maximum and absolute minimum values of f on the given interval.\r
\n" ); document.write( "\n" ); document.write( "f(x) = 6x^3 − 18x^2 − 54x + 1,
\n" ); document.write( "[−2, 4] \n" ); document.write( "

Algebra.Com's Answer #701126 by Fombitz(32388) $\"\"$ $\"About$

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\n" ); document.write( "Take the derivative and set it equal to each other to find extrema,
\n" ); document.write( " $\"df%2Fdx=18x%5E2-36x-54\"$
\n" ); document.write( " $\"18x%5E2-36x-54=0\"$
\n" ); document.write( " $\"x%5E2-2x-3=0\"$
\n" ); document.write( " $\"%28x-3%29%28x%2B1%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"x-3=0\"$
\n" ); document.write( " $\"x=3\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x%2B1=0\"$
\n" ); document.write( " $\"x=-1\"$
\n" ); document.write( "Take the second derivative to find which is which,
\n" ); document.write( " $\"d2f%2Fdx2=2x-2\"$
\n" ); document.write( "At $\"x=-1\"$ , $\"2x-2=2%28-1%29-2=-4\"$ so the maximum occurs here.
\n" ); document.write( "At $\"x=3\"$ , $\"2x-2=2%283%29-2=4\"$ so the minimum occurs here.\r
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