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I have a question that relates to 14.7 from the Stewart Calculus book regarding absolute max...

I have a question that relates to 14.7 from the Stewart Calculus book regarding absolute max and min of a triangular region. Boundaries of triangle: y=x, x=0, y=4, and the function is: f(x,y) = x^2-xy+y^2+1

I got as far as finding the critical point of (0,0) solving for fx=0 and fy = 0, but I am struggling to find the critical points along the boundary and solve the rest of the problem. Any help would be appreciated :)

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