Answer
the absolute maximum is 17 at (0, 4) and
(4, 4), and the absolute minimum is 1 at (0, 0).
Work Step by Step
(i) On 2 OA D x y D y y , ( , ) (0, ) 1 on 0 4; y
D y y y D (0, ) 2 0 0; (0, 0) 1 and
D(0, 4) 17
(ii) On 2 AB D x y D x x x , ( , ) ( , 4) 4 17 on
0 4; ( , 4) 2 4 0 2 x D x x x and
(2, 4) is an interior point of ; (2, 4) 13 AB D and
D D (4, 4) (0, 4) 17
(iii) On 2 OB D x y D x x x , ( , ) ( , ) 1 on 0 4; x ( , ) 2 0 0 D x x x x and y 0, which is not an
interior point of OB; endpoint values have been found above
(iv) For interior points of the triangular region, ( , ) 2 0 xf x y x y and ( , ) 2 0 0 yf x y x y x and
y 0, which is not an interior point of the region. Therefore, the absolute maximum is 17 at (0, 4) and
(4, 4), and the absolute minimum is 1 at (0, 0).
