document.write( "Question 200749: Find all the points of inflection of the function
\n" ); document.write( "f(x)=8x^2-2x^4
\n" ); document.write( "find point with smaller x-value
\n" ); document.write( "find point with larger x value
\n" ); document.write( "can someone help please\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #150987 by Earlsdon(6294)\"\" \"About 
You can put this solution on YOUR website!
The graph of this function \"f%28x%29+=+8x%5E2-2%5E4\"will give you the answers:
\n" ); document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C8%2C8x%5E2-2x%5E4%29\"
\n" ); document.write( "But you can also get the answers algebraically:
\n" ); document.write( "\"f%28x%29+=+8x%5E2-2x%5E4\" Substitute \"y+=+f%28x%29\"
\n" ); document.write( "The roots (zeros) occur at y = 0, so substitute this...
\n" ); document.write( "\"8x%5E2-2x%5E4+=+0\" Solve for the x's, there should be four roots for this 4th degree polynomial. Factor out \"2x%5E2\"
\n" ); document.write( "\"%282x%5E2%29%284-x%5E2%29+=+0\" Apply the zero product rule so that...
\n" ); document.write( "\"2x%5E2+=+0\" or \"4-x%5E2+=+0\"
\n" ); document.write( "For \"2x%5E2+=+0\", \"x+=+0\" There are two roots at x = 0.
\n" ); document.write( "For \"4-x%5E2+=+0\", \"x%5E2+=+4\" then \"x+=+2\" and \"x+=+-2\"
\n" ); document.write( "So the four roots (zeros) are:
\n" ); document.write( "\"highlight%28x+=+0%29\"
\n" ); document.write( "\"highlight_green%28x+=+0%29\"
\n" ); document.write( "\"highlight%28x+=+2%29\"
\n" ); document.write( "\"highlight_green%28x+=+-2%29\"
\n" ); document.write( "Compare these with the graph!
\n" ); document.write( "The inflection points (where the curve changes sign) are:
\n" ); document.write( "\"x+=+-sqrt%282%29\"
\n" ); document.write( "\"x+=+0\"
\n" ); document.write( "\"x+=+sqrt%282%29\"
\n" ); document.write( "My appologies for the first answer about the points of inflection! \n" ); document.write( "
\n" );