Below is the correct code for the false$-$position method. Using the image provided modify this code to create a script for the modified false$-$position method. $($Focus on highlighted parts$)$The limitation of the False$-$position method is its one$-$sidedness. If the root is close to

either upper or lower bound, one of the bracketing points is keep fixed. To overcome this

issue, the modified false$-$position method was developed. The pseudo code for the

modified false$-$position method is shown down below.

$=>$ Fill the right column in the table below with your script

clc; clear all; close all;

$\%$ Parameters

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

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

es $=5$e$-10$; $\%$ 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$2,$ iter$2]=$ FalsePosition$($xl$,$ xu$,$ es$,$ imax$)$

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

$\%$ Initialization

iter $=0$;

xr $=$ xl;

ea $=100$;

$\%$ Graph shows $35$ iterations for iter $1$:$35$

for iter $=1$:$35$

$\%$ Step $2$: update root

xrold $=$ xr;

xr $=$ xu $-($f$($xu$)*($xl $-$ xu$))/($f$($xl$)-$ f$($xu$))$;

$\%$ Step $3$: error

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

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

end

$\%$ Plot relative error

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

$\%$ Step $4$: Update Boundary

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

if test $<mtext\; id="EditorElement\_235059"></mtext><mn\; id="EditorElement\_235060">0</mn>$

xu $=$ xr;

elseif test $>0$

xl $=$ xr;

else

ea $=0$;

end

$\%$ Break if tolerance is reached

if ea $$ es

break;

end

end

xx $=$ xr;

end

$\%\%$ Function Evaluation

function $[$fc$]=$ f$($x$)$

g $=9\mathrm{.}81$;

m $=68\mathrm{.}1$;

t $=10$;

fc $=$ g $*$ m $/$ x $*(1-$ exp$(-$x $/$ m $*$ t$))-40$;

end