Define f :
R2→R by
f(x, y) = x
2 + 2y
2 - x for (x, y) ∈
R2.
Let D = {(x, y) ∈
R2 ∶ x
2 + y
2 ≤ 1} and
E={(x,y)∈R2:4x2+9y2≤1}.Consider the sets
D
max = {(a, b) ∈ D ∶ f has absolute maximum on D at (a, b)},
D
min = {(a, b) ∈ D ∶ f has absolute minimum on D at (a, b)},
E
max = {(c, d) ∈ E ∶ f has absolute maximum on E at (c, d)},
E
min = {(c, d) ∈ E ∶ f has absolute minimum on E at (c, d)}.
Then the total number of elements in the set
D
max ∪ D
min ∪ E
max ∪ E
minis equal to _________.