Consider the equation in MATLAB : $x^3+2x=sin(x)+1$ and using Secant method.

Write a computer program to approximate the root of the equation in two cases:

$($i$)x_0=0\mathrm{.}5,x_1=0\mathrm{.}6$ to within accuracy ${10}^{-15}.$

$($ii$)x_0=0,x_1=1$ to within accuracy ${10}^{-15}.$

The decimal places to the right of the decimal point must be at least $15$ places.