document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=350476>Question 350476</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: Consider the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=+root%283%2Cx%29+ ALIGN=MIDDLE  ALT=\"+f%28x%29=+root%283%2Cx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%3C=x%3C=8+ ALIGN=MIDDLE  ALT=\"+1%3C=x%3C=8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "a) Find the average value of f on the interval [1, 8].\r<BR>\n" );
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document.write( "b) Find c such that fave. = f (c).\r<BR>\n" );
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document.write( "c) Sketch the graph of f and a rectangle whose area is the same as the area under<BR>\n" );
document.write( "the graph of f . </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #250534 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=250534\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: Consider the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=+root%283%2Cx%29+ ALIGN=MIDDLE  ALT=\"+f%28x%29=+root%283%2Cx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%3C=x%3C=8+ ALIGN=MIDDLE  ALT=\"+1%3C=x%3C=8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "a) Find the average value of f on the interval [1, 8].<BR>\n" );
document.write( "For the average value on this interval you will use:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28int%28root%283%2C+x%29%2C+dx%2C+1%2C+8%29%29%2F%288-1%29 ALIGN=MIDDLE  ALT=\"%28int%28root%283%2C+x%29%2C+dx%2C+1%2C+8%29%29%2F%288-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Writing the radcial in fractional exponent form will probably help with finding the integral:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28int%28x%5E%281%2F3%29%2C+dx%2C+1%2C+8%29%29%2F%288-1%29 ALIGN=MIDDLE  ALT=\"%28int%28x%5E%281%2F3%29%2C+dx%2C+1%2C+8%29%29%2F%288-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The indefinite integral of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F3%29dx ALIGN=MIDDLE  ALT=\"x%5E%281%2F3%29dx\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%284%2F3%29%2F%284%2F3%29+%2B+C+=+%283x%5E%284%2F3%29%29%2F4+%2B+C ALIGN=MIDDLE  ALT=\"x%5E%284%2F3%29%2F%284%2F3%29+%2B+C+=+%283x%5E%284%2F3%29%29%2F4+%2B+C\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The definite integral, from 1 to 8, will be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%288%29%5E%284%2F3%29%29%2F4+-+%283%281%29%5E%284%2F3%29%29%2F4 ALIGN=MIDDLE  ALT=\"%283%288%29%5E%284%2F3%29%29%2F4+-+%283%281%29%5E%284%2F3%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E%284%2F3%29+=+8%5E%28%281%2F3%29%2A4%29+=+%288%5E%281%2F3%29%29%5E4+=+2%5E4+=+16 ALIGN=MIDDLE  ALT=\"8%5E%284%2F3%29+=+8%5E%28%281%2F3%29%2A4%29+=+%288%5E%281%2F3%29%29%5E4+=+2%5E4+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So now we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2816%29%29%2F4+-+3%2F4 ALIGN=MIDDLE  ALT=\"%283%2816%29%29%2F4+-+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2F4+-+3%2F4 ALIGN=MIDDLE  ALT=\"48%2F4+-+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2F4 ALIGN=MIDDLE  ALT=\"45%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the average value is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2845%2F4%29%2F7+=+45%2F28 ALIGN=MIDDLE  ALT=\"%2845%2F4%29%2F7+=+45%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "b) Find c such that fave. = f (c).<BR>\n" );
document.write( "So we solve:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28c%29+=+45%2F28 ALIGN=MIDDLE  ALT=\"f%28c%29+=+45%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+c%29+=+45%2F28 ALIGN=MIDDLE  ALT=\"root%283%2C+c%29+=+45%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cube both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+91125%2F21952 ALIGN=MIDDLE  ALT=\"c+=+91125%2F21952\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "c) Sketch the graph of f and a rectangle whose area is the same as the area under the graph of f.<BR>\n" );
document.write( "The graph of f (without the limited domain) looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C+400%2C+-1%2C+11%2C+-1%2C+5%2C+x%5E%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C+400%2C+-1%2C+11%2C+-1%2C+5%2C+x%5E%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note:<ul><li>Truncate this graph so that only the part between x = 1 and x = 8 shows.</li><li>I think the intention is for the graph of the rectangle to be on the same graph. Specifically, the bottom of the rectangle should be the on the x axis between 1 and 8 and the sides will be 45/28 in height extending up from the x axis (at x = 1 and x = 8). If done well, the top of the rectangle should intersect the graph of f at x = c =  91125/21952 (which is approximately 4.15)</li></ul> </SPAN>\n" );
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