Question $3($Root$-$finding: Bisection and Secant methods$)$

$3\mathrm{.}1$ Given: $f(x)=x^3-x-1$

$($a$)$ Verify that $f(x)$ has a root in the interval $1,2.$

$($b$)$ Use the Bisection method to determine the approximate root. Do four iterations.

$(3)$

$(10)$

$($c$)$ Use any available tool show $10$ iterations.

$(5)$

$3\mathrm{.}2$ Use the secant method to find the root of the function given in question $3\mathrm{.}1$