HW$7\_2$ Let $f(x)=xcos(x)-xsin(x).$

a$)$ determine the true value of $f^{\text{'}}(x)$ at $x=2\mathrm{.}9,3\mathrm{.}0,3\mathrm{.}1,3\mathrm{.}2$

b$)$ evaluate the function $f(x)$ at the same $4$ points

c$)$ Use the results from b$)$ to estimate the derivative at all points using forward $(O(h)),$ backward $)$

and centered $)$ formulas $($where possible$)$

d$)$ compute $e_t,$ the true relative errors

e$)$ compute the first derivatives at the first and the last points using $3-$point, $O(h^2)$ forward and backward

formulas respectively. Also include $e_t$ calculations.

f$)$ calculate the second derivative using appropriate $)$ formulas at $x=2\mathrm{.}9,3\mathrm{.}0,3\mathrm{.}1,3\mathrm{.}2$

Present your results in a table.

Note: $e_t=|\frac{\text{T}\text{r}\text{u}\text{e}-\text{A}\text{p}\text{p}\text{r}\text{o}\text{x}}{\text{T}\text{r}\text{u}\text{e}}|100\%$

please do d$,$e$,$f

no coding! Thank you!