In this question, numerical approaches for the first$-$order and second$-$order derivatives will be considered. Please refer to the codes provided in the module on CANVAS.

The changing of position $x$ of an object with respect to time $t$ is given by the following function $($over the time period $0t10s)$:

$x(t)=5t^3+2t^2+3t+2$

Providing evidence of your approach in a spreadsheet or word document, using the provided code for forward, backward and central difference method, determine the velocity of the object at $t=4s$ considering step sizes $h=1,0\mathrm{.}1$ and $0\mathrm{.}01.$ Compare the accuracy and cost of the approach. How do the results compare to the analytical solutions?

Furthermore, providing evidence of your approach in a spreadsheet or word document, using the provided code for forward, backward and central difference methods, determine the acceleration of the object at $t=6s$ considering step sizes $h=1,0\mathrm{.}1$ and $0\mathrm{.}01.$ Compare the accuracy and cost of the approach. How do the results compare to the analytical solutions?