Question 987875
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Hello,

your post was written incorrectly from the Perl's point of view.

I corrected and saved it.

You can submit it again with my corrections.
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OK.  Now I am continuing to solve it.


f(x) - f(a) = {{{(x^3+11)}}} - {{{(a^3+11)}}} = {{{x^3-a^3}}} = {{{(x-a)*(x^2 + ax + a^2)}}}.


{{{(f(x) - f(a))/(x-a)}}} = {{{((x-a)*(x^2 + ax + a^2))/(x-a)}}} = {{{(x^2 + ax + a^2)}}}. 


It is the expression for for the slope of the tangent line to the curve  {{{y}}} = {{{x^3 + 11}}}  in vicinity of the point  (a,f(a).


If the point &nbsp;<B>x</B>&nbsp; tends to the point &nbsp;<B>a</B>, &nbsp;then the slope tends to &nbsp;{{{a^2 + a^2 + a^2}}} = {{{3a^2}}}. 


Thus &nbsp;&nbsp;{{{M[a]}}} = {{{3a^2}}}.