Q$1)$For function peak below, you are given a list that ascends up to some maximum value and then descends from there

until the end of the list.

For example, the list $2,5,8,12,15,7,4,3,1$ is allowed but

$5,9,14,7,6,10$ is not.

a$)$Develop a recursive algorithm that finds the maximum element in such a list. $($No sorting or modifying the list$).(15$p$)$

b$)$ Write the recurrence relation for the algorithm. $(10$p$)$

c$)(10$p$)$Find the closed for of the following recurrence

$T(n)=\{\begin{array}{cc}2,& n=1\\ 3T(2n)+n,& n>1\end{array}$