Consider the polynomial () = −0.14 − 0.153 − 0.52 − 0.25 + 1.2

The true value of its derivative at x=0.5 is ′

(0.5) = −0.9125. Use backward, forward, and centered

first finite differences to estimate the derivative numerically if the step size ∆ = 0.25, and determine

the percent error between the true value and each of the estimated values (percent error is given by

= −

converted to a percentage.) What value of ∆ would you have to use for the backward and forward

finite differences to get the same percent error as the centered finite difference (hint: it should be less

than 0.25.)