Consider the following function:

$f(x)=x^3+3e^{-3x}$

Calculate the derivative $d\frac{f}{d}x$ at $x=3$ numerically with the fourth$-$order centered differences formulation

$(O(h^4))$ using:

$1$a$.$ The points $x=-1,x=1,x=5,$ and $x=7.$

$1$b$.$ With $h=1.$

$1$c$.$ Calculate the true percentage error for $(1$a$)$ and $(1$b$).$

Notes: Show your work. Use at least $4$ significant digits and rounding in all your calculations. Do not use

MATLAB or Python in your calculations.