Fixed Point Method, Newton$-$Raphson Method, & Secant Method

Determine the highest real root of $f_5(x)=2x^3-11\mathrm{.}7x^2+17\mathrm{.}7x-5$ :

Graphically $($Just for checking out$)$

Use fixed point iteration method $($three iterations, $x_0=2\mathrm{.}9).$

save the root on HW$4\_1.$dat file

save the estimated error ${}_a$ on HW$4\_2.$dat file

show all steps of three iterations by hands. $($use an engineering paper.$)$

Use Newton$-$Rapson method $($three iterations, $x_0=2\mathrm{.}9).$

save the root on $HW43.$dat file

save the estimated error ${}_a$ on HW$4\_4.$dat file

show all steps of three iterations by hands. $($use an engineering paper.$)$

Use Secant method $($three iterations, $x_{-1}=2\mathrm{.}9,x_0=4).$

save the root on HW$4\_5.$dat file

save the estimated error ${}_a$ on HW$4\_6.$dat file

show all steps of three iterations by hands. $($use an engineering paper.$)$