Consider the function f$($x$)=$ x$($cos x $$ sin x$)$

a$)$ Evaluate the function at four points: x $=2\mathrm{.}9,3\mathrm{.}0,3\mathrm{.}1,3\mathrm{.}2$

b$)$ Use the results from a$)$ to estimate the first derivative at same points using $1$st order forward or backward

difference $($as appropriate$).$ Thereafter, calculate the true error et$.$

c$)$ Now compute the first derivative using $2$nd order central difference. For end point use $2$nd order forward

or backward as appropriate. Calculate the true error again for this case.

d$)$ How does the true error in b$)$ compare to that in c$)$

e$)$ Compute the second derivative using second order formulas. Calculate the true error for this case also.

Repeat problem $1($with all parts$)$ in PYTHON this time. However, instead of the four points, use $21$ points,going from $x=2$ to $x=4,$ i$.$e$.,x=2,2\mathrm{.}1,2\mathrm{.}2,$dots$4$ for each part.

Instead of reporting the raw values, make plots of function, derivatives, $e_t,$ etc. vs$.x$ in each part.