Chapter 5, Problem 10P

Find the positive real root of $f\left(x\right)=x^4-8x^3-{35}^2+450x-1001$ using the false-position method. Use initial guesses of $x_l=4.5\text{ and }{x}_u=6$ and perform five iterations. Compute both the true and approximate errors based on the fact that the root is 5.60979. Use a plot to explain your results and perform the computation to within ${\epsilon }_s=1.0\%$.