document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912785>Question 912785</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Howdy, having a little problem with this question, not sure if it's supposed to be a piecewise function or what.\r<BR>\n" );
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document.write( "The question goes:\r<BR>\n" );
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document.write( "The graph of f is concave down for 0<=x<=6. Which is bigger, (f(3)-f(1))/(3-1) or (f(5)-f(3))/(5-3)? Why?\r<BR>\n" );
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document.write( "Not exactly sure how you'd go about solving this; Most of the book before this has given a formula or a table to use, this question does not.\r<BR>\n" );
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document.write( "Pardon if this is in the wrong section, it looks like a function and I'm not quite certain if I'm supposed to be solving it, or graphing, or what.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #554051 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=554051\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This function's interval of [0,6] has been split up into these two intervals: [1,3] and [3,5]\r<BR>\n" );
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document.write( "It turns out that the slopes of the secant lines will be decreasing in a concave down section of a graph. It's somewhat connected to the idea that the tangent line slopes are decreasing.\r<BR>\n" );
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document.write( "Since the interval [1,3] is to the left of [3,5], this means (f(3)-f(1))/(3-1) will be larger. Both slopes are negative, but (f(3)-f(1))/(3-1) is closer to 0, therefore larger.\r<BR>\n" );
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document.write( "Imagine the flip scenario: say  (f(5)-f(3))/(5-3) is larger. This would mean that the slopes are increasing, but this would mean you're on a concave up section of the graph. So this contradicts what we're given.\r<BR>\n" );
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document.write( "Hopefully it's making sense.\r<BR>\n" );
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document.write( "Let me know if you need more help or if you need me to explain a step in more detail.<BR>\n" );
document.write( "Feel free to email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a><BR>\n" );
document.write( "or you can visit my website here: <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">http://www.freewebs.com/jimthompson5910/home.html</a>\r<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Jim  </SPAN>\n" );
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