Approximate the Optimal Trust T $($in kN$)$ by iterating on the root of f$($T$)$ using the three methods

below. You picked the initial brackets $/$ guess$($es$)$ below based only on knowledge that these kits

tend to sell for somewhere around $20$ kN$.$

Do two iterations for each method, accurate to at least $4$ decimals $($yes$,$ I know that$$s a fraction of a

penny, but go with it$).$By$-$hand$$ still means you should use your calculator for all the hard

arithmetic $($multiplying and dividing$),$ but I want to see all your steps: write out the formulae you

are using and key values as you iterate so I can confirm you$$re doing the process correctly.

$($i$)$ Bisection: start with the bracket a $=0\mathrm{.}50,$ b $=40$ and calculate the midpoints T$1$ and T$2,$

clearly justifying $($based on the signs of f$($T$))$ how the a$$s and$/$or b$$s are changing

after both iterations.

$($ii$)$ Secant: start with T$1=0\mathrm{.}5$ and T$2=40.$ Calculate T$3$ and T$4.$

$($iii$)$ N$-$R: start with T$1=20.$ Calculate T$2$ and T$3.$