# Science:Math Exam Resources/Courses/MATH105/April 2016/Question 01 (d)/Solution 1

Suppose that ${\displaystyle f(x,y)=x+y}$ and that the domain of ${\displaystyle f}$ is ${\displaystyle [0,1]^{2}}$ (i.e., the set of points ${\displaystyle (x,y)}$ satisfying ${\displaystyle 0\leq x\leq 1}$ and ${\displaystyle 0\leq y\leq 1}$).
Since ${\displaystyle 0\leq x\leq 1}$ and ${\displaystyle 0\leq y\leq 1}$, clearly ${\displaystyle f}$ has an absolute minimum of ${\displaystyle 0+0=0}$ at ${\displaystyle (0,0)}$ and an absolute maximum of ${\displaystyle 1+1=2}$ at ${\displaystyle (1,1)}$.
However, neither ${\displaystyle (0,0)}$ nor ${\displaystyle (1,1)}$ is a critical point of ${\displaystyle f}$ because ${\displaystyle \nabla f=(\partial _{x}f,\partial _{y}f)=(1,1)}$ (recall that a critical point of ${\displaystyle f}$ is a point ${\displaystyle (x,y)}$ at which ${\displaystyle \nabla f(x,y)=(0,0)}$).