document.write( "Question 361533: Find the absolute maximum and absolute minimum values of the function below. If an absolute maximum or minimum does not exist, enter NONE.
\n" ); document.write( "f(x) = x^2 + 432/x on the open interval (0, infinity) \n" ); document.write( "

Algebra.Com's Answer #257752 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
An absolute minimum exists at x = 6.
\n" ); document.write( " $\"y+=+x%5E2+%2B+432%2Fx\"$ ,
\n" ); document.write( " $\"dy%2Fdx=+2x-432%2Fx%5E2\"$ . Letting this derivative equal 0, and solving,
\n" ); document.write( "we get $\"2x+=+432%2Fx%5E2\"$ , or $\"x%5E3+=+216\"$ , or x = 6.
\n" ); document.write( "Now $\"d%5E2y%2Fdx%5E2+=+2%2B864%2Fx%5E3\"$ . Substitute x = 6 into the 2nd derivative to find out that $\"d%5E2y%2Fdx%5E2%3E0\"$ . Therefore there is an absolute minimum at x = 6. \n" ); document.write( "

\n" );