document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173487>Question 1173487</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the function give below:<BR>\n" );
document.write( "f(x)=2x^4+ax^3-4x^2+bx-18<BR>\n" );
document.write( "It is known that f(2)=4 and that f(1)=0<BR>\n" );
document.write( "G. Determine the instantaneous rate of change when x =1<BR>\n" );
document.write( "H. Estimate the turning points and then find the slope at these turning points. Are your estimation correct?<BR>\n" );
document.write( "I. Which of these turning point you estimated are maximum and which are the minimum?<BR>\n" );
document.write( "(please explain and show your working) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #798869 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=798869\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)=2x^4+ax^3-4x^2+bx-18<BR>\n" );
document.write( "f(2)=4=32+8a-16+2b-18<BR>\n" );
document.write( "so 6=8a+2b<BR>\n" );
document.write( "f(1)=0=2+a-4+b-18<BR>\n" );
document.write( "so 20=a+b<BR>\n" );
document.write( "a=20-b<BR>\n" );
document.write( "6=160-8b+2b<BR>\n" );
document.write( "-154=-6b<BR>\n" );
document.write( "b=25 2/3<BR>\n" );
document.write( "-<BR>\n" );
document.write( "b=20-a<BR>\n" );
document.write( "6=8a+40-2a<BR>\n" );
document.write( "-34=6a<BR>\n" );
document.write( "a=-5 2/3<BR>\n" );
document.write( "-<BR>\n" );
document.write( "The function is f(x)=2x^4-(17/3)x^3-4x^2+(77/3)x-18<BR>\n" );
document.write( "When x=1 f'(x)=8x^3-17x^2-8x+(77/3) and f(1)=8-17-8+77/3=8 2/3 units, instantaneous rate of change.<BR>\n" );
document.write( "f(1)=0 so equation of tangent line at (1, 0) is y=(26/3)x-26/3<BR>\n" );
document.write( "set derivative equal to 0.<BR>\n" );
document.write( "8x^3-17x^2-8x+(77/3)-18=0<BR>\n" );
document.write( "try 0 and slope is 7 2/3 so no turning point<BR>\n" );
document.write( "at  x=-1 slope is still positive<BR>\n" );
document.write( "but at x=-2 the slope is strongly negative<BR>\n" );
document.write( "estimate the turning point (a local minimum) between x=-1 and x=-2 (it is at x=-1.19)<BR>\n" );
document.write( "-<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-55%2C50%2C2x%5E4-%2817%2F3%29x%5E3-4x%5E2%2B%2877%2F3%29x-18%2C%2826x%2F3%29-%2826%2F3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );