(approximation in differences for the derivative) it is possible to approximate the derivative of a function f (x) evaluated at a point xi with the form in differences backwards
(df /dx )*(xi) ≈ f (xi) - f (xi − 1)/( xi - xi − 1 )= ∆f /∆x
if f (x) = 25x3 - 6x2+ 7x - 88 y ∆x = xi - xi − 1 = 0.2 approximate the value of the derivative at xi = 2 and calculate the true error (et)made by the estimate.