Chapter 4, Problem 20P

Consider the function $f\left(x\right)=x^3-2x+4$ on the interval $\left[-2,2\right]\text{ with }h=0.25$. Use the forward, backward, and centered finite difference approximations for the first and second derivatives so as to graphically illustrate which approximation is most accurate. Graph all three first derivative finite difference approximations along with the theoretical, and do the same for the second derivative as well.