document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155520>Question 1155520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the Mean Value Theorem applies to the function f(x)=7-x^2 on the interval [-1,2]. if so, find the points that are guaranteed to exist by Mean Value  Theorem.  </SPAN>\n" );
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document.write( "The given function is a polynomial; it is everywhere continuous and differentiable, so the MVT applies.<br><BR>\n" );
document.write( "f(-1) = 6; f(2) = 3; the two endpoints of the specified interval are (-1,6) and (2,3).<br><BR>\n" );
document.write( "The slope of the secant determined by those two points is -1.<br><BR>\n" );
document.write( "We need to find the point(s) in the specified interval where the derivative is equal to -1.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%2Fdx+=+-2x+=+-1 ALIGN=MIDDLE  ALT=\"df%2Fdx+=+-2x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+.5 ALIGN=MIDDLE  ALT=\"x+=+.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The point that is guaranteed by the MVT is (.5,6.75).<br><BR>\n" );
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