$($Problem $1-$ use Excel$)$

For this problem, use the following data file on Canvas:

HW$3$P$1\_$Data.xIsx

The data set represents a reactor's shell temperature as

it is being quenched over a span of $80$ minutes, and you

wish to examine the time rate of temperature change

$(d\frac{T}{d}t)$ for the system.

$($a$)$ Using this data and a second$-$order finite $($central$)$

difference formula for the first derivative,

$\frac{df(x_i)}{dx}$~~$\frac{f(x_{i+1})-f(x_{i-1})}{2x}$

approximate the time rate of temperature change

$($where possible$)$ in Column C$.$ Highlight the rate at $10$

minutes.

$($b$)$ Create a user function in VBA to approximate the

second derivative, $(d^2\frac{T}{d}{t}^2),$ using the following

second$-$order finite $($central$)$ difference formula:

$\frac{d^{2}f(x_i)}{d{x}^2}$~~$\frac{f(x_{i+1})-2f(x_i)+f(x_{i-1})}{(x{)}^2}$

Place your results $($where possible$)$ in Column D$.$

Highlight the second derivative approximation at $10$

minutes.

$($c$)$ Display the entire VBA code resulting from your

programmed user function created for part $($b$).$ Include

your name as a comment.