document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168096>Question 168096</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm Having hard time solving  this homework. Can anyone help?\r<BR>\n" );
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document.write( "2.  Calculate the points of the tangent of the curve  : y = ex(x2 – 8) where and in which the tangent line is horizontal\r<BR>\n" );
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document.write( "3. Write one of the two tangents to the curve : y = 1 + x³   which are parallel to this equation 12x - y = 1.\r<BR>\n" );
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document.write( "4.  Calculate\r<BR>\n" );
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document.write( "I) If  f(x) = ex cos x calculate f ’(x) et f ’’\r<BR>\n" );
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document.write( "(ii) Calculate (d99/ dx99) Sin x\r<BR>\n" );
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document.write( "5.\r<BR>\n" );
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document.write( "Calculate the derivative :\r<BR>\n" );
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document.write( " I) y = xe-x²\r<BR>\n" );
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document.write( "II) Let say:  r(x) = f(g(h(x))) whit h(1) = 2, g(2) = 3, h’(1)= 4, g’(2) = 5, f’(3) = 6. Calculate r’(1).\r<BR>\n" );
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document.write( "III) Show that the function : y = Ae-x + Be-x satisfy the equation with differential y”+ 2y’+y = 0\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123882 by </B><A HREF=/tutors/aboutme.mpl?userid=oscargut><B>oscargut(2103)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oscargut><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=oscargut><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123882\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi here i answered questions 2) and 3) contact me if you need more help\r<BR>\n" );
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document.write( "2. Calculate the points of the tangent of the curve : y = ex(x2 – 8) where and in which the tangent line is horizontal\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=exp%28x%5E2-8%29 ALIGN=MIDDLE  ALT=\"y=exp%28x%5E2-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=2x%2Aexp%28x%5E2-8%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=2x%2Aexp%28x%5E2-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "y'=0 if only if x=0\r<BR>\n" );
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document.write( "then the point is (0,0) (where the tangent of the curve is horizontal)\r<BR>\n" );
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document.write( "3. Write one of the two tangents to the curve : y = 1 + x³ which are parallel to this equation 12x - y = 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x-y=1 ALIGN=MIDDLE  ALT=\"12x-y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+12x-1 ALIGN=MIDDLE  ALT=\"y+=+12x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1%2Bx%5E3 ALIGN=MIDDLE  ALT=\"y+=+1%2Bx%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=3x%5E2 ALIGN=MIDDLE  ALT=\"dy%2Fdx=3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then 12 (first term of 12x-1 and y'(x)= 3x^2 are the same}\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+=+3x%5E2 ALIGN=MIDDLE  ALT=\"12+=+3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=4 ALIGN=MIDDLE  ALT=\"x%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "taking x=2 then equation of the line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28dy%2Fdx%29%2A%282%29%28x-2%29%2By%282%29 ALIGN=MIDDLE  ALT=\"y+=+%28dy%2Fdx%29%2A%282%29%28x-2%29%2By%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%28x%29=1%2Bx%5E3 ALIGN=MIDDLE  ALT=\"y%28x%29=1%2Bx%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+12%28x-2%29%2B9=12x-15 ALIGN=MIDDLE  ALT=\"y+=+12%28x-2%29%2B9=12x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+12x-15 ALIGN=MIDDLE  ALT=\"y+=+12x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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