Chapter 6, Problem 14P

Use (a) the Newton-Raphson method and (b) the modified secant method $\left(\delta =0.05\right)$ to determine a root of $f\left(x\right)=x^5-16.05x^4+88.75x^3-192.0375x^2+116.35x+31.6875$ using an initial guess of $x=0.5825\text{ and }{\epsilon }_s=0.01\%$. Explain your results.