document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=197410>Question 197410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Estimate the instantaneous rate of change: <BR>\n" );
document.write( "a.for the function y = x^2 at the following x values: <BR>\n" );
document.write( "i.x = 1 <BR>\n" );
document.write( "ii.x = 2 <BR>\n" );
document.write( "iii.x = 3 <BR>\n" );
document.write( "b.for the function y = x^3 at the following x values: <BR>\n" );
document.write( "iv.x = 1 <BR>\n" );
document.write( "v.x = 2 <BR>\n" );
document.write( "vi.x = 3 <BR>\n" );
document.write( "c.Create two functions that can be developed from a) and b) that will give you the instantaneous rate of change without reducing the interval. <BR>\n" );
document.write( "d.Use the reasoning from c) to find the instantaneous rate of change for: <BR>\n" );
document.write( "iv.y = x^4 at x = 3 <BR>\n" );
document.write( "v.y = 3x^3 at x = 2 <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148201 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=148201\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Estimate the instantaneous rate of change: <BR>\n" );
document.write( "a.for the function y = x^2 at the following x values: <BR>\n" );
document.write( "The rate of change is 2x.<BR>\n" );
document.write( "i.x = 1<BR>\n" );
document.write( "m = 2<BR>\n" );
document.write( "ii.x = 2<BR>\n" );
document.write( "m = 4<BR>\n" );
document.write( "iii.x = 3<BR>\n" );
document.write( "m = 6<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "b.for the function y = x^3 at the following x values:<BR>\n" );
document.write( "The rate of change, m, is 3x^2<BR>\n" );
document.write( "iv.x = 1<BR>\n" );
document.write( "m = 3<BR>\n" );
document.write( "v.x = 2<BR>\n" );
document.write( "m = 12<BR>\n" );
document.write( "vi.x = 3<BR>\n" );
document.write( "m = 27<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "c.Create two functions that can be developed from a) and b) that will give you the instantaneous rate of change without reducing the interval.<BR>\n" );
document.write( "I did that, it's the 1st derivative.<BR>\n" );
document.write( "For y = x^2, y' = 2x<BR>\n" );
document.write( "For y = x^3, y' = 3x^2<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "d.Use the reasoning from c) to find the instantaneous rate of change for: <BR>\n" );
document.write( "iv.y = x^4 at x = 3<BR>\n" );
document.write( "y' = 4x^3<BR>\n" );
document.write( "m at 3 = 108<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "v.y = 3x^3 at x = 2<BR>\n" );
document.write( "y' = 9x^2<BR>\n" );
document.write( "m at 2 = 36<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );