Use a loop to iteratively update the values of the four variables above as described below. This loop should

continue to execute until the absolute value of val$1$ and val$2$ are both less than $0\mathrm{.}000001.$ Each time the loop

executes, perform the following steps:

$$ Increment n$.$

$$ Create a variable named new$\_$x that is equal to the average of x$1$ and x$2.$

$$ Create a variable named new$\_$val that is equal to f$($new$\_$x$).$

$$ If new$\_$val is negative, then set x$1$ to new$\_$x and set val$1$ to new$\_$val. Otherwise, set x$2$ to new$\_$x

and set val$2$ to new$\_$val