Question

Define f : $\R^2 → \R$ by
f(x, y) = x2 + 2y2 - x for (x, y) ∈ $\R^2$.
Let D = {(x, y) ∈ $\R^2$ ∶ x2 + y2 ≤ 1} and E=\left\\{(x,y)\in \R^2:\frac{x^2}{4}+\frac{y^2}{9} \le 1\right\\}.
Consider the sets
Dmax = {(a, b) ∈ D ∶ f has absolute maximum on D at (a, b)},
Dmin = {(a, b) ∈ D ∶ f has absolute minimum on D at (a, b)},
Emax = {(c, d) ∈ E ∶ f has absolute maximum on E at (c, d)},
Emin = {(c, d) ∈ E ∶ f has absolute minimum on E at (c, d)}.
Then the total number of elements in the set
Dmax ∪ Dmin ∪ Emax ∪ Emin
is equal to _________.

Answer 1

The correct answer is : 5.