document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203773>Question 1203773</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x) = x^2 + 5\r<BR>\n" );
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document.write( "a) f(-6) =\r<BR>\n" );
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document.write( "b) Find if f(x) = 14\r<BR>\n" );
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document.write( "c) f(x + h) =\r<BR>\n" );
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document.write( "d) Calculate: f(x + h) - f(x) over h\r<BR>\n" );
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document.write( "Can you please explain to me this homework question by showing the step-by-step calculations? Thank you!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839603 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = x^2 + 5\r<BR>\n" );
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document.write( "a.<BR>\n" );
document.write( "f(-6) = (-6)^2 + 5 = 36 + 5 = 41.<BR>\n" );
document.write( "x is replaced by -6.\r<BR>\n" );
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document.write( "b.<BR>\n" );
document.write( "f(x) = 14.<BR>\n" );
document.write( "this means that x^2 + 5 = 14<BR>\n" );
document.write( "subtract 5 from both sides of the equation to get x^2 = 9.<BR>\n" );
document.write( "solve for x to get x = 3<BR>\n" );
document.write( "f(3) = 3^2 + 5 = 14.\r<BR>\n" );
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document.write( "c.<BR>\n" );
document.write( "f(x) = x^2 + 5<BR>\n" );
document.write( "f(x+h) = (x+h)^2 + 5<BR>\n" );
document.write( "you are replacing (x) with (x+h)<BR>\n" );
document.write( "f(x+h) = (x+h)^2 + 5 = x^2 + 2hx + h^2 + 5\r<BR>\n" );
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document.write( "d.<BR>\n" );
document.write( "Calculate: f(x + h) - f(x) over h<BR>\n" );
document.write( "from (c), you have f(x+h) = x^2 + 2hx + h^2 + 5<BR>\n" );
document.write( "subtract f(x) from that and divide by h to get:<BR>\n" );
document.write( "(f(x+h) - f(x)) / h = (x^2 + 2hx + 5 + h^2 - x^2 - 5) / h<BR>\n" );
document.write( "simplify to get (2hx + h^2) / h<BR>\n" );
document.write( "simplify further to get 2x + h.\r<BR>\n" );
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document.write( "this might be easier to see in the attached worksheet.\r<BR>\n" );
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document.write( "the limit as h approaches 0 becomes 2x.<BR>\n" );
document.write( "this is the derivative of x^2 + 5.<BR>\n" );
document.write( "you will learn this later, if you haven't already.<BR>\n" );
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