document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=564698>Question 564698</A>: <I><SPAN STYLE=\"word-break: break-all;\"> let f(x)= e^(x^2). at how many points in the closed interval [3,-3], does the instantaneous rateof change of f equal the average rate of change of f?<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 #365441 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=365441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\Delta(y)}{\Delta(x)} = \frac{e^{3^2} - e^{(-3)^2)}}{3 - (-3)} = 0\">\r<BR>\n" );
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document.write( "Hence we want to find all points in [-3,3] such that f'(x) = 0. By the chain rule, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f'(x) = 2xe^{x^2}\">\r<BR>\n" );
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document.write( "This is equal to zero only when x = 0 (since e^(x^2) can never equal zero). There is only one point that satisfies. </SPAN>\n" );
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