document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=476981>Question 476981</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f (x) = 2x^2 + 8x-1\r<BR>\n" );
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document.write( "(a) Find the derivative f ’ of f. \r<BR>\n" );
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document.write( "(b) Find an equation of the tangent line to the point of (1,3). \r<BR>\n" );
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document.write( "(c) Determine whether the critical point gives maximum or minimum f value and find the value. \r<BR>\n" );
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document.write( "Do appreciate your help. Thanking you in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #327023 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=327023\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) f'(x) = 4x+8\r<BR>\n" );
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document.write( "(b)  (1,3) is NOT a point on the parabola.  \r<BR>\n" );
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document.write( "(c) You don't need calculus to know if there is a max or a min, it's obvious from the coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > that the function has an (absolute) min.\r<BR>\n" );
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document.write( "BUT if you insist, then f'(x) = 4x+8 = 0 ==> x = -2.\r<BR>\n" );
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document.write( "The 2nd derivative is f\"(x) = 4 > 0, so by the 2nd derivative test there is (absolute) min at x = -2.  (x = -2 could have been gotten using the good ol' formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.) </SPAN>\n" );
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