QUESTION $2$

Consider the function $f(x,y)=x^2-xy+y^2$ defined over the triangular region with vertices at $(0,0),(1,0)$ and $(0,1).$ The location of the global minimum of this function is

a$.(0,0)$

b$.(1,0)$

c$.(\frac{1}{2},\frac{1}{2})$

d$.(0,1)$

e$.(\frac{1}{4},\frac{1}{4})$