mubashirmansoor said:The expresion shows a fact when "x" is either minima or maxima;
0 = 10^10*tan(.5(tan-1((f(x+.01)-f(x))/10^8)+tan-1((f(x)-f(x-.01))/10^8)))
-( f(x+0.01) - f(x) ) = ( f(x) - f(x-0.01) )
which means: f(x+0.01)=f(x-0.01)
which is a general truth, (& I think a prove to the validity of the technique)
and since no one has pointed this out yet, this would only be a proof that the technique works when you have an extremum at [itex]x[/itex] (ie. when you already know the derivative is 0). And even then, as we've shown you, your technique still won't give the exact derivative of 0 in many cases, because [itex]f[/itex] isn't always symmetric about turning points.