document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180565>Question 1180565</A>: <I><SPAN STYLE=\"word-break: break-all;\"> function: y= x^4-8x^3-16x+5<BR>\n" );
document.write( "a. Identify range<BR>\n" );
document.write( "b. find x-intercept (you can solve this using the intermediate value theorem to estimate where the roots will be, I'm just not sure how to do that exactly) <BR>\n" );
document.write( "c. find critical numbers<BR>\n" );
document.write( "d. points of extreme with the first derivative test for the interval of increasing and decreasing testing<BR>\n" );
document.write( "- please show the work, I did some work on my own but I think I messed up in some steps. thank you very much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810322 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=810322\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would graph it first. Clearly +oo is the upper bound <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-600%2C100%2Cx%5E4-8x%5E3-16x%2B5%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-600%2C100%2Cx%5E4-8x%5E3-16x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We know that when x=0 y=5, and as x increases from 0, the function will be decreasing, since subtracting the cube of a small positive number and the first power of a small positive number will both be larger than the adding the fourth power of that number.<BR>\n" );
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document.write( "So one root will be between 0 and 1, closer to 0<BR>\n" );
document.write( "when x=8, the x^4 and -8x^3 terms will cancel, making the function -123. Therefore, the next root will be somewhat larger than 8 and well below 9 (closer to 8).<BR>\n" );
document.write( "The other two roots will be complex.<BR>\n" );
document.write( "The critical values are at x=0.2996 and x=8.227. The function is continuous.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "The derivative is y'=4x^3-24x^2-16<BR>\n" );
document.write( "set that equal to 0 and divide by 4, and the is x^3-6x^2-4=0<BR>\n" );
document.write( "this is negative when x=6 and positive when x=7, so the local minimum is when x is in between those two points.<BR>\n" );
document.write( "x=6.11<BR>\n" );
document.write( "-<BR>\n" );
document.write( "So the range is (-523.8679, +oo)<BR>\n" );
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