Develop a computer program to find the root of the following function:

P $=(-$m$+4)$e$-0\mathrm{.}5$m $-2$

using the following three methods:

$($a$)$ Bisection $($initial guesses of ml $=0\mathrm{.}5$ and mu $=1\mathrm{.}5).$

$($b$)$ Newton$-$Raphson $($initial guess of m$0=1\mathrm{.}5).$

$($c$)$ Secant $($initial guesses of m$-1=0\mathrm{.}2$ and m$0=0\mathrm{.}7).$

Perform iterations until the approximate percent relative error falls below $0\mathrm{.}005\%.$ For this problem, it is Mandatory to use MatLab. However, you are not allowed to use any built$-$in functions in MatLab that are not available in the other compilers. $>>\%$ Function definition

P $=$ @$($m$)($m $+4)*$ exp$(-0\mathrm{.}5*$ m$)-2$;

$\%$ Bisection method

ml $=0\mathrm{.}5$;

mu $=1\mathrm{.}5$;

max$\_$iterations $=1000$;

tolerance $=0\mathrm{.}00005$; $\%0\mathrm{.}005\%$ as a decimal

for i $=1$:max$\_$iterations

fm $=$ P$($ml$)$;

fu $=$ P$($mu$)$;

m $=($ml $+$ mu$)/2$;

fp $=$ P$($m$)$;

$\%$ Check for convergence

if abs$($fp$)<$ tolerance

break;

end

$\%$ Update interval

if fm $*$ fp $<0$

mu $=$ m;

else

ml $=$ m;

end

end

fprintf$(\text{'}$Bisection Method: Root $=\%\mathrm{.}6$f$,$ Iterations $=\%$d

$\text{'},$ m$,$ i$)$;

$\%$ Newton$-$Raphson method

m$0=1\mathrm{.}5$;

for i $=1$:max$\_$iterations

f$0=$ P$($m$0)$;

f$0\_$prime $=($P$($m$0+0\mathrm{.}0001)-$ P$($m$0))/0\mathrm{.}0001$; $\%$ Numerical derivative

m$1=$ m$0-$ f$0/$ f$0\_$prime;

$\%$ Check for convergence

if abs$(($m$1-$ m$0)/$ m$1)<$ tolerance

break;

end

m$0=$ m$1$;

end

fprintf$(\text{'}$Newton$-$Raphson Method: Root $=\%\mathrm{.}6$f$,$ Iterations $=\%$d

$\text{'},$ m$1,$ i$)$;

$\%$ Secant method

m$\_$minus$1=0\mathrm{.}2$;

m$0\_$secant $=0\mathrm{.}7$;

for i $=1$:max$\_$iterations

f$\_$minus$1=$ P$($m$\_$minus$1)$;

f$0\_$secant $=$ P$($m$0\_$secant$)$;

m$1\_$secant $=$ m$0\_$secant $-$ f$0\_$secant $*($m$0\_$secant $-$ m$\_$minus$1)/($f$0\_$secant $-$ f$\_$minus$1)$;

$\%$ Check for convergence

if abs$(($m$1\_$secant $-$ m$0\_$secant$)/$ m$1\_$secant$)<$ tolerance

break;

end

m$\_$minus$1=$ m$0\_$secant;

m$0\_$secant $=$ m$1\_$secant;

end ANS: fprintf$(\text{'}$Secant Method: Root $=\%\mathrm{.}6$f$,$ Iterations $=\%$d

$\text{'},$ m$1\_$secant, i$)$;

Bisection Method: Root $=1\mathrm{.}500000,$ Iterations $=1000$

Newton$-$Raphson Method: Root $=2\mathrm{.}292386,$ Iterations $=4$

Secant Method: Root $=2\mathrm{.}292386,$ Iterations $=5.$ as last expert gave me the code and when i performed it is showing that $1000$ iterations in bisection and soon for other methods. but his sample results is just showing $18$ iterations. so can i get a proper solution that how many iterations will be required and allong with the answers of all the iterations.