Consider the polynomial (x) = −0.1x 4 − 0.15x 3 − 0.5x 2 − 0.25x + 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 for the step size ∆x = 0.25, and determine the percent error between the true value and each of the estimated values (percent error is given by = − mconverted to a percentage.) What value of ∆x 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.)?