Consider the Booth function, which is convex. It takes in a vector $=\left[\begin{array}{c}{}_1\\ {}_2\end{array}\right]$ and

returns a scalar:

$B()=({}_1+2{}_2-7{)}^2+(2{}_1+{}_2-5{)}^2$

$($a$)$ Derive an expression for $gra{d}_{}B()$

$($b$)$ Use your answer to $($a$)$ to solve $minimis{e}_{}B()$ analytically