Find the $s$ value which maximizes following function $T(s),$

$T=\frac{15s(1-s)}{(1-s)(4s^2-3s+4)}$

a$.)$ graphically,

b$.)$ analytically,

c$.)$ find the solution taking an $=0\mathrm{.}05$ with the Golden$-$Section Search Method

i$.$ Perform two iterations by hand

ii$.$ Perform all iterations by Matlab algorithm

d$.)$ find the solution taking an initial tolerance tol $=0\mathrm{.}01,$ and initial guess t $0=0\mathrm{.}5$ with

the Newton's method

iii. Perform two iterations by hand

iv$.$ Perform all iterations by Matlab algorithm