f(x) x2 2 and g(x) 3x2 1 For the above function, use base point x0 1 0 and x 0 1 to compute f and g Find (fg) (the change in the product) by computing f(x0 x)g(x0 x) f(x0)g(x0) Check that (fg) g(x0)f f(x0)g f g Try the same with x 0 01 and see whether the term f g becomes very small ...

f 021 g 063 and fg 24423 This is equal to gx 0 ...

f(x) = x2 + 2 and g(x) = 3x2 - 1. For the above function, use base

Question:

f(x) = x2 + 2 and g(x) = 3x2 - 1.
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.