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Find the absolute maximum and minimum of $f(x,y)=4x^2+2xy-2y^2$ on the unit square $0x2,0y2.$

A$)$ maximum $4,$ minimum $0$

B$)$ maximum $\frac{13}{3},$ minimum $-3$

C$)$ maximum $\frac{13}{2},$ minimum $-4$

D$)$ maximum $\frac{13}{3},$ minimum $0$

E$)$ maximum $4,$ minimum $-3$