1. Consider the function $f(x) = x(\cos x - \sin x)$\\
a) Evaluate the function at four points: $x = 2.9, 3.0, 3.1, 3.2$\
b) Use the results from a) to estimate the first derivative at same points using 1st order forward or backward\\difference (as appropriate). Thereafter, calculate the true error $e_t$.\
c) Now compute the first derivative using 2nd order central difference. For end point use 2nd 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.\
Tabulate all your results. Note: $e_t = \frac{|true\ value - approx\ value|}{true\ value} \times 100\%$\
2. 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., $x = 2, 2.1, 2.2, ...4$ for each part.\
Instead of reporting the raw values, make plots of function, derivatives, $e_t$, etc. vs. $x$ in each part.
