This problem studies the second derivative of the following function in python:

f$($x$)=1$ cos x$/($x$^2)$

We take x $=0\mathrm{.}004.$

$($a$)$ Start by analytically evaluating the second derivative, and plugging in x $=0\mathrm{.}004.$

$($b$)$ Let h take on the values $101,102,...,106$ and produce a log$-$log plot of the absolute error in the first central$-$difference approximation to the second derivative.

$($c$)$ Introduce a new set of points to the previous plot, this time evaluating the first

central$-$difference approximation to the second derivative not of f$($x$),$ but of the

analytically rewritten version you arrived at in the previous chapter $($recall: you had

used a trigonometric identity which enabled you to avoid the cancellation$).($All in python code$)$