document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=858205>Question 858205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I am terrible at systems of equations and I have an applications of derivatives assignment with a few questions, the only one dealing with systems of equations is as follows:\r<BR>\n" );
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document.write( "For the function f(x)= ax^4 + bx^3 - 4x^2 + 2cx + 14<BR>\n" );
document.write( "Determine the values of a, b, and c, such that,<BR>\n" );
document.write( "f(-2)=2 , f'(-2)=16 , and f''(-2)=-8\r<BR>\n" );
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document.write( "I have tried only messing around with various numbers in my calculator for the past hour to get any number to match with the given values, and I failed\r<BR>\n" );
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document.write( "Any help would be much appreciated<BR>\n" );
document.write( "Thanks  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #517103 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=517103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For the function f(x)= ax^4 + bx^3 - 4x^2 + 2cx + 14<BR>\n" );
document.write( "Determine the values of a, b, and c, such that,<BR>\n" );
document.write( "f(-2)=2 , f'(-2)=16 , and f''(-2)=-8 <BR>\n" );
document.write( "-------<BR>\n" );
document.write( "f(x)= ax^4 + bx^3 - 4x^2 + 2cx + 14<BR>\n" );
document.write( "f(-2) = 16a - 8b -16 - 4c + 14 = 2<BR>\n" );
document.write( "16a - 8b - 4c = 4<BR>\n" );
document.write( "4a - 2b - c = 1  Eqn 1<BR>\n" );
document.write( "----<BR>\n" );
document.write( "f(x)= ax^4 + bx^3 - 4x^2 + 2cx + 14<BR>\n" );
document.write( "f'(x) = 4ax^3 + 3bx^2 - 8x + 2c<BR>\n" );
document.write( "f'(-2) = -32a + 12b + 16 + 2c = 16<BR>\n" );
document.write( "16a - 6b - c = 0  Eqn 2<BR>\n" );
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document.write( "f''(x) = 12ax^2 + 6bx - 8<BR>\n" );
document.write( "f''(-2) = 48a - 12b - 8 = -8<BR>\n" );
document.write( "4a - b = 0  Eqn 3<BR>\n" );
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document.write( "b = 4a<BR>\n" );
document.write( "Sub for b in Eqns 1 & 2<BR>\n" );
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document.write( "4a - 2b - c = 1  Eqn 1<BR>\n" );
document.write( "4a - 8a - c = 1<BR>\n" );
document.write( "4a + c = -1    Eqn A<BR>\n" );
document.write( "---<BR>\n" );
document.write( "16a - 6b - c = 0  Eqn 2<BR>\n" );
document.write( "16a - 24a - c = 0<BR>\n" );
document.write( "8a + c = 0<BR>\n" );
document.write( "c = -8a<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Sub for c in Eqn A<BR>\n" );
document.write( "4a + c = -1    Eqn A<BR>\n" );
document.write( "4a - 8a = -1<BR>\n" );
document.write( "a = 1/4<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "c = -2<BR>\n" );
document.write( "b = -1 </SPAN>\n" );
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