Consider the function $f(x_1,x_2)=x_1^2+x_2^2-4x_1{x}_2$

a$)$ View $x_1$ as a variable and $x_2$ as a constant. Determine whether $f$ is convex in $x_1$ and

prove it$.$

b$)$ View $x_2$ as a variable and $x_1$ as a constant. Determine whether $f$ is convex in $x_2$ and

prove it$.$

c$)$ View $f$:$R^{2}R$ as a function of the input vector $(x_1,x_2).$ Determine whether $f$ is convex

in $(x_1,x_2)$ and prove it$.$

Hints: For a$)$ and b$),$ treat one variable as a constant, and calculate the second$-$order

derivative of a single$-$variable function.