How do I determine the maximum or the minimum of in the range the function $f(x,y)=x^3+y^3 $in the range $B=\left \{ \left ( x,y \right ):x^2+y^2\leq 1 \right \}$?

As a continuous function f must have (the entire area) in B a maximum and a minimum. How do I show that they can lie on the outskirts of B. How do I examine the behavior of f at the edge of B?

I know that $f\_x=3x^2,f\_y=y=3y^2,f\_{xx}=6x, f\_{yy}=6y, f\_{xy}=0$.

I have calculated that minimum and maximum are in point $(0,0)$.Saddle point is $(0,0)$.

Problem is I but do not know how to show max and min in the interval, and examine the behavior in function?