Chapter 6, Problem 9P

Determine the highest real root of $f\left(x\right)=x^3-6x^2+11x-6.1$:

(a) Graphically.

(b) Using the Newton-Raphson method (three iterations, $x_i=3.5)$.

(c) Using the secant method (there iterations, $x_{i+1}=2.5\text{ and }{x}_i=3.5$).

(d) Using the modified secant method (three iterations, $x_i=3.5,\delta =0.01$)