5. Consider the following 5-point finite difference:

5. Consider the following 5-point finite difference: f" ( x) = wif(x - 2h) + waf(x - h) + waf ( x) + wif ( x + h) + w;f (x + 2h). (a) Find w, wa, wa, w, and w; so that the finite difference approximation of f"(x) has maximum order of accuracy. Explicitly write out the error term for this finite difference approximation. (b) Add the effect of round-off error and use this to estimate the optimal grid spacing h that minimizes the total error (truncation error + round-off error)