Thanks for all the comments and suggestions. While searching on Numberical differentiation, I have found something really helpful in the maths components I already had, it uses an exotic technique called Solvitsky-Golvay filtering to smooth the data.

Here are the same views as before, but using the new code. Data is processed from vectors, sawtooth holds the original data, smoothedfirstdiff, smootherseconddiff hold the results.

 mysqlrows:=0;
   WITH mytable2 DO
     BEGIN
       mysqlrows:=recordcount;
     if mysqlrows <>0 THEN
      BEGIN
       Sawtooth.Clear;
       Smoothedfirstderiv.Clear;
       SmoothedSecondDeriv.Clear;
       sawtooth.NrOfElem           :=mysqlrows-1;
       smoothedfirstderiv.NrOfElem :=mysqlrows-1;
       smoothedsecondderiv.NrofElem:=mysqlrows-1;
       For ctr:=1 to mysqlrows-1  DO
        BEGIN
        {Load sawtooth vector with data}
         sawtooth.Elem[ctr]:=fields[1].Value;
         next;
        END;
       {vector now filled with data}

       firstderiv (sawtooth,0,mysqlrows-1,smoothedfirstderiv  ,round(filtersize.value));
       secondderiv(sawtooth,0,mysqlrows-1,smoothedsecondderiv ,round(filtersize.Value));
       {Data is now smoothed in vector, put it into t_pressuretime, the SQL table with the data}

       first;
       for CTR := 1 to mysqlrows-1 do
         BEGIN
          edit;
          fields[2].Value:=10*smoothedfirstderiv. Elem[ctr]; //Scaled up for the graph;
          fields[3].Value:=10*smoothedsecondderiv.Elem[ctr];
          next;
         END;
       showmessage('Done data transfer');
      END
       ELSE
        showmessage('Failed');
     myquery1.Execute;
     END;
 

Here's the graph



Now I have a very clear indication of the maximum.