document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=428180>Question 428180</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. f(x)= x^3 - 3x^2 + x + 1<BR>\n" );
document.write( "2. f(x)=sinx + 1 on [-2pi, 2pi]<BR>\n" );
document.write( "3. f(x)=(x^2)(e^(-4x))\r<BR>\n" );
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document.write( "(a) Find the x- and y-intercepts of the function.<BR>\n" );
document.write( "(b) Draw a number line for f:<BR>\n" );
document.write( "(c) Find all critical numbers for f prime:<BR>\n" );
document.write( "(d) Draw a number line for f prime:<BR>\n" );
document.write( "(e) Find all zeros of f double prime:<BR>\n" );
document.write( "(f) Draw a number line for f double prime:<BR>\n" );
document.write( "(h) Find all inflection points of f:<BR>\n" );
document.write( "(i) Sketch the graph of f. Label all inflection points. Label your axes. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #297764 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=297764\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll get you started:\r<BR>\n" );
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document.write( "If f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+=+3x%5E2+%2B+x+%2B+1 ALIGN=MIDDLE  ALT=\"x%5E3+=+3x%5E2+%2B+x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then f'(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+1 ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and f''(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x ALIGN=MIDDLE  ALT=\"6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > (simply applying the power rule).\r<BR>\n" );
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document.write( "If f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29%2B1 ALIGN=MIDDLE  ALT=\"sin%28x%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > then f'(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and f''(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sin%28x%29 ALIGN=MIDDLE  ALT=\"-sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "#3 is a little harder to differentiate because we need to apply the product rule twice. If f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%28e%5E%28-4x%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%28e%5E%28-4x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > then f'(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%28e%5E%28-4x%29%29+-+4%28x%5E2%29%28e%5E%28-4x%29%29+=+e%5E%28-4x%29%282x+-+4x%5E2%29 ALIGN=MIDDLE  ALT=\"2x%28e%5E%28-4x%29%29+-+4%28x%5E2%29%28e%5E%28-4x%29%29+=+e%5E%28-4x%29%282x+-+4x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Differentiating again, f''(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4e%5E%28-4x%29%282x+-+4x%5E2%29+%2B+e%5E%28-4x%29%282+-+8x%29+=+e%5E%28-4x%29%28-8x+%2B+16x%5E2+%2B+%282+-+8x%29%29+=+e%5E%28-4x%29%2816x%5E2+-+16x+%2B+2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >. I'll let you handle the 24 parts of the problem. </SPAN>\n" );
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