Given an approximation xn$1$ to a root of a function f $($x$),$ the Newton$-$Raphson method

tries to find a better approximation to the root by computing

xn $=$ xn$1$

f $($xn$1)$

f $($xn$1)$

where f $($x$)$ is the derivative of f $($x$).$

The Newton$-$Raphson method computes an approximation to a root as follows:

$1.$ An appropriate initial extimate of the root x$0$ and error tolerance $\backslash$epsi are selected.

$2.$ If the current estimate xi is within the preselected error tolerance of the root, this is returned

as the final estimate. This can be checked by seeing if the function changes sign in the interval

$[$xi $\backslash$epsi $,$ xi $\backslash$epsi $].$

$3.$ A revised estimate of the root is calculated using the above formula and step $2$ is repeated, using the

revised estimate.

In a new worksheet and module, within the same workbook complete the following steps.

$$ Use Excel to graph the function f $($x$)=($x $1)5($x $2)3$ over an appropriate interval using

$200$ steps.

$$ Write code to implement the Newton$-$Raphson method.

$$ You should use $\backslash$epsi $=105$ as your tolerance.

$$ Your code should ask the user for values of x$0$ and $\backslash$epsi $($either from the spreadsheet or using input

boxes$)$ and display the final approximation and the number of iterations computed $($either on the

spreadsheet or using a message box$).$

$$ Use your code to estimate the root of the function.

$$ Note f $($x$)=5($x $1)43($x $2)2$