document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=412400>Question 412400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi! \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+-%284%2F3%29x%5E2+%2B+12x ALIGN=MIDDLE  ALT=\"f%28x%29=+-%284%2F3%29x%5E2+%2B+12x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Can you prove that: if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%3Cb%3C=9%2F2+ ALIGN=MIDDLE  ALT=\"+a%3Cb%3C=9%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > so we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%29%3Cf%28b%29 ALIGN=MIDDLE  ALT=\"f%28a%29%3Cf%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Whith that, I'll determine the slope of the function.\r<BR>\n" );
document.write( "\n" );
document.write( "I tried at first to calculate f(b)-f(a), but I don't know what to do after that...\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you and sorry for bad English.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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 #289679 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=289679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+9%2F2 ALIGN=MIDDLE  ALT=\"x+%3C+9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the function has a positive slope, since the vertex is at 9/2 and the x^2 coefficient is negative. We can say that the function is *strictly increasing* on this interval, so if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3C+b+%3C=+9%2F2 ALIGN=MIDDLE  ALT=\"a+%3C+b+%3C=+9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%29+%3C+f%28b%29 ALIGN=MIDDLE  ALT=\"f%28a%29+%3C+f%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );