Let f(x, y) = 2x - 4xy+2y+1 be defined over the tri- angular region x = 0, y = 0, x - y = 1. The absolute minimum of f is (I) and occurs at the point (II,III). The absolute maximum of f is (IV) and occurs at the point (V,VI). Which of the following is correct? I: -1, II: 0, III: -1, IV: 3, V: 1, VI: 0 I: -1, II: -1, III: 2, IV: 4, V: 1, VI: 0 I: -1, II: -1, III: 3, IV: 5, V: 1, VI : 0 I: -1, II: 1, III: 4, IV: 6, V: 1, VI: 0 I: -1, II: 1, III: 5, IV: 7, V: 1, VI: 0 (a) (b) (c) (d) (e)​