document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=702267>Question 702267</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that f\"(x)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-2 ALIGN=MIDDLE  ALT=\"3x%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=-1 ALIGN=MIDDLE  ALT=\"f%282%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , f'(-1)=5 , find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "I need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=steps ALIGN=MIDDLE  ALT=\"steps\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=THANKS%21 ALIGN=MIDDLE  ALT=\"THANKS%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #432875 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=432875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f '' (x) = 3x^2 - 2\r<BR>\n" );
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document.write( "Integrate both sides to get\r<BR>\n" );
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document.write( "f ' (x) = x^3 - 2x + C\r<BR>\n" );
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document.write( "We're told that f ' (-1) = 5, so\r<BR>\n" );
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document.write( "f ' (x) = x^3 - 2x + C\r<BR>\n" );
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document.write( "f ' (-1) = (-1)^3 - 2(-1) + C\r<BR>\n" );
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document.write( "5 = -1 + 2 + C\r<BR>\n" );
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document.write( "5 = 1 + C\r<BR>\n" );
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document.write( "5 - 1 = C\r<BR>\n" );
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document.write( "4 = C\r<BR>\n" );
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document.write( "C = 4\r<BR>\n" );
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document.write( "So f ' (x) = x^3 - 2x + 4\r<BR>\n" );
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document.write( "Integrate both sides to get\r<BR>\n" );
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document.write( "f(x) = (1/4)*x^4 - x^2 + 4x + C\r<BR>\n" );
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document.write( "Now use the fact that f(2) = -1\r<BR>\n" );
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document.write( "f(x) = (1/4)*x^4 - x^2 + 4x + C\r<BR>\n" );
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document.write( "f(2) = (1/4)*(2)^4 - (2)^2 + 4(2) + C\r<BR>\n" );
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document.write( "f(2) = (1/4)*(16) - 4 + 4(2) + C\r<BR>\n" );
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document.write( "f(2) = 4 - 4 + 8 + C\r<BR>\n" );
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document.write( "f(2) = 8 + C\r<BR>\n" );
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document.write( "-1 = 8 + C\r<BR>\n" );
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document.write( "-1 - 8 = C\r<BR>\n" );
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document.write( "-9 = C\r<BR>\n" );
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document.write( "C = -9\r<BR>\n" );
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document.write( "Therefore, the function f(x) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+expr%281%2F4%29%2Ax%5E4+-+x%5E2+%2B+4x+-+9 ALIGN=MIDDLE  ALT=\"f%28x%29+=+expr%281%2F4%29%2Ax%5E4+-+x%5E2+%2B+4x+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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