Here is the code given for the bisection method:

clc;

clear all;

close all;

$\%$ Parameters

xl $=12$; $\%$ lower bound

xu $=16$; $\%$ upper bound

es $=5$e$-2$; $\%$ tolerance

imax $=1000$; $\%$ max iteration

$\%$ Initialization of the plot

figure;

xlabel$(\text{'}$Iteration$\text{'})$;

ylabel$(\text{'}$Approximate Relative Error $(\%)\text{'})$;

title$(\text{'}$Error vs Iterations'$)$;

hold on;

xlim$([035])$;

set$($gca$,$ 'YScale', 'log'$)$;

grid on;

$\%$ Find root

$[$xx$1,$ iter$1]=$ Bisect$($xl$,$ xu$,$ es$,$ imax$)$;

$\%$ Bisection Method

function $[$xx$,$ iter$]=$ Bisect$($xl$,$ xu$,$ es$,$ imax$)$

$\%$ Initialization

iter $=0$;

xr $=$ xl;

ea $=100$;

$\%$ Graph shows $35$ iterations

for iter $=1$:$35$

$\%$ Step $2$: update root

xrold $=$ xr;

xr $=($xl $+$ xu$)/2$;

$\%$ Step $3$: error

if xr ~$=0$ && iter $>1$

ea $=$ abs$(($xr $-$ xrold$)/$ xr$)*100$;

end

$\%$Plot relative error

semilogy$($iter$,$ ea$,\text{'}$bo$\text{'})$;

$\%$ Step $4$: Update Boundary

test $=$ f$($xl$)*$ f$($xr$)$;

if test $<mtext\; id="EditorElement\_2351587"></mtext><mn\; id="EditorElement\_2351588">0</mn>$

xu $=$ xr;

elseif test $>0$

xl $=$ xr;

else

ea $=0$;

end

end

xx $=$ xr;

end

Part $1$:

Modify the MATLAB script of the Bisection Method function for the False$-$position Methodwith minimum function evaluations. You may read about minimum function evaluation in textbook page $135,$ section $5\mathrm{.}3\mathrm{.}2.$ The only diIerence between the Bisection and False$-$position method is how you get the root at each iteration in step $2.=>$ Fill the right column in the table below with your script

Bisection Method $-\frac{x_l+x_u}{2}$

False Position Method: $\frac{f(x_u)(x_l-x_u)}{f(x_l)-f(x_u)}$