Use Python and Matlab for all questions below $($unless some derivation is required which you can do

better by hand$).$ If using Python, use Jupyter notebook to format properly, comment when necessary,

and include all required and necessary outputs $($Jupyter allows LATEX embedding which would be

great if you could use it$).$ Convert the notebook to pdf and upload to blackboard against the assignment.

If using MATLAB, use MATLAB publish to convert to pdf$.$ Solution documents should be well

commented.

Q$1.$ Consider the vectors

$v(r)=sin(r)+r^2+1$

$($a$)$ Find the expressions for $\frac{dv}{dr},\frac{d^{2}v}{d{r}^2},\frac{d^{3}v}{d{r}^3}$

$($b$)$ Plot $v$ in the range $-r.$ v should be on the vertical axis and $r$ should be on the

horizontal axis

$($c$)$ Through visual inspection of the plot, determine the value of $r$ for which $v$ is minimum

$($d$)$ Plot $w=\frac{dv}{dr}$ for $-r.$ At what value of $r$ is $w=0?$ How does this answer compare with

the answer in part c$?$ If the answers the close to each other, explain why? PLEASE USE ONLY MATLAB AND SOLVE BY HANDED IF NEEDED