document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156000>Question 1156000</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this calculus 1 max and min question<BR>\n" );
document.write( "I just cant find the min, the max I got was 1.39<BR>\n" );
document.write( "Find the absolute maximum and absolute minimum values of f on the given interval. (Round your answers to two decimal places.)<BR>\n" );
document.write( "f(x) = ln(x^2 + x + 2)<BR>\n" );
document.write( "[-1, 1] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #778716 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=778716\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe i have the answer you're looking for.<BR>\n" );
document.write( "as you indicated, the maximum value is 1.386 rounded to 3 decimal places.  this occurred at x = 1.<BR>\n" );
document.write( "this i was able to determine by graphing the equation and looking for the maximum value.<BR>\n" );
document.write( "using my calculator, i was able to determine that the maximum value was 1.386294361 rounded to the number of digits the calculator was able to display.<BR>\n" );
document.write( "it was evident from the graph that x = 1 was the highest point in the interval from -1 to 1.<BR>\n" );
document.write( "using the same graph, i was able to determine that the minimum value was.56 when x = .5.<BR>\n" );
document.write( "i then looked up the first derivative of ln(x^2 + x + 2).  <BR>\n" );
document.write( "according to the derivative calculator i found on the web, it was (2x + 1) / (x^2 + x + 2).<BR>\n" );
document.write( "i set this equal to 0 and solved for x to get x = -1/2.<BR>\n" );
document.write( "when x = -1/2, i used a calculator on the original equation to get the value of .5596157879 rounded to the number of decimal digits the calculator was able to display.<BR>\n" );
document.write( "i used information that i got from the web and used a graphing calculator to determine what the answer should be.<BR>\n" );
document.write( "since i didn't really know how to find the derivative of the ln function, i did a little research on the web and came up with the following reference that you might find useful.<BR>\n" );
document.write( "that reference is <a  rel=nofollow HREF= \"http://www.ltcconline.net/greenl/courses/116/explog/logderivative.htm\" target = \"_blank\">http://www.ltcconline.net/greenl/courses/116/explog/logderivative.htm</a><BR>\n" );
document.write( "it's a little dificult to follow with all the dy/dx jargon, but the general idea is that the derivative of ln(x) = 1/x and the derivative of an expression within the parentheses of ln(x), such as ln(3x-4) involves the chain rule and winds up being the derivative of 3 divided by 3x-4.<BR>\n" );
document.write( "if you extrapolate from this example, you see that the derivative of ln(x^2 + x + 2) is the derivative of x^2 + x + 2 divided by x^2 + x + 2.<BR>\n" );
document.write( "this winds up being 2x + 1 divided by x^2 + x + 2.<BR>\n" );
document.write( "here's what the graph looks like.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/041401.jpg\" alt=\"$$$\" ><BR>\n" );
document.write( "here's what the output of the derivative calculator looks like.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/041402.jpg\" alt=\"$$$\" ><BR>\n" );
document.write( "the calculator can be found at <a  rel=nofollow HREF= \"https://www.desmos.com/calculator\" target = \"_blank\">https://www.desmos.com/calculator</a><BR>\n" );
document.write( "the derivative calculator can be found at <a  rel=nofollow HREF= \"https://www.derivative-calculator.net/\" target = \"_blank\">https://www.derivative-calculator.net/</a><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );