f(x) = 2x + 3 and g(x) = -3x + 2.
For the above function, use base point x0 = 1.0 and Δx = 0.1 to compute Δf and Δg. Find Δ (fg) (the change in the product) by computing f(x0 + Δx)g(x0 + Δx) - f(x0)g(x0). Check that Δ(fg) = g(x0)Δf + f(x0)Δg + Δf Δg. Try the same with Δx = 0.01 and see whether the term Δf Δg becomes very small.