The Mathematical Background

Try it for yourself. I constructed the example using the algebraic formula

Output = 10*Labor - 0.0055*Labor^2

You can set up a spreadsheet to explore the example if you wish. To create a range of labor input values, put your beginning value in the top cell and program the cell below to compute the top cell plus the number you want to use for Labor. Then use the "fill down" or similar command to fill in the range of labor values below the beginning two values. In the column just to the right, put the formula above, replacing "Labor" with a reference to the corresponding cell in the first column. That will give the output values in the second column. Then put a formula in the second and lower cells of the third column that gives the quotient of that row minus the previous row for the second column (Output) over that row minus the previous row for the first column (Labor). The corresponding marginal productivity approximations will then be shown in the third column. So try it yourself.