document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1076744>Question 1076744</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 	i. Evaluate the function f(t) = t^3/3 – 2t^2 &#8722; 45t + 58 for extreme values and classify them. \r<BR>\n" );
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document.write( "ii. What is the value of t at the point of inflection?\r<BR>\n" );
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document.write( "Please assist\r<BR>\n" );
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document.write( "Thank you\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #691368 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=691368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have to calculate derivatives.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%2Fdt=t%5E2-4t-45=%28t-9%29%28t%2B5%29 ALIGN=MIDDLE  ALT=\"df%2Fdt=t%5E2-4t-45=%28t-9%29%28t%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That derivative function is<BR>\n" );
document.write( "negative for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%3Ct%3C9 ALIGN=MIDDLE  ALT=\"-5%3Ct%3C9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(meaning f(t) decreases in that interval);<BR>\n" );
document.write( "it is zero at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-5 ALIGN=MIDDLE  ALT=\"t=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=9 ALIGN=MIDDLE  ALT=\"t=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(indicating local extreme values of the function),<BR>\n" );
document.write( "and the derivative is positive for any other <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > value<BR>\n" );
document.write( "(indicating that f(t) is increasing).<BR>\n" );
document.write( "So, f(t) increases with t for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%3C-5 ALIGN=MIDDLE  ALT=\"t%3C-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "reaches a local maximum at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-5 ALIGN=MIDDLE  ALT=\"t=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "decreases until reaching a local minimum at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=9 ALIGN=MIDDLE  ALT=\"t=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and then increases for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%3E9 ALIGN=MIDDLE  ALT=\"t%3E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "There is no absolute minimum or maximum.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28t-%3Einfinity%2Cf%28t%29%29 ALIGN=MIDDLE  ALT=\"lim%28t-%3Einfinity%2Cf%28t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28t-%3E-infinity%2Cf%28t%29%29=-infinity ALIGN=MIDDLE  ALT=\"lim%28t-%3E-infinity%2Cf%28t%29%29=-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "For inflection points,<BR>\n" );
document.write( "we need the second derivative.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2f%2Fdt%5E2=2t-4=2%28t-2%29 ALIGN=MIDDLE  ALT=\"d%5E2f%2Fdt%5E2=2t-4=2%28t-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "shows you that the inflection point is at<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2 ALIGN=MIDDLE  ALT=\"t=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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