Problem $2(15$ points$)($Core Course Outcomes $5$ & $11)/($M$)$at labGrader

Consider the function

f$($x$)-$cos$($x$),$

where the argument is in radians, and its analytical second derivative

$($d$^(2))/($dx$^(2))$f$($x$)--$cos$($x$)$

defined on the interval x evaluated at M$\_($k$)+1$ equally spaced points x$\_($i$)$ where M$\_($k$)-2^($k$).$ Use function

mySecondDerivativeOrder $3$ to calculate the crror e$\_($i$)$ of the finite difference approximation of d$^(2)($f$)/($d$)$x$^(2)$ at each point x$\_($i$).$

For k$-7,8,9,$dots,$20,21,$ plot the entry$-$wise $3-$norm L$\_($k$)$ of the error e$\_($i$)($see Exam $2)$ as a function of h$\_($k$)$ using a logarithmic

scale for both L$\_($k$)$ and h$\_($k$).$

Notes for the MatlabGrader script submission:

Comment out clear or clear all in your script when submitting to MatlabGrader.

Generate and store the figure handle examFigl for the graph before doing any plotting commands, using

examFigl $=$ figure$(1)$;

Properly label both axis using the appropriate variable names $($h$,$L$).$

Do not include the source code for any functions in your script submission. Necessary functions are provided on Matlab$-$

Grader.