The Lagrangian is
with critical points where the partial derivatives vanish.
Substitute into the last equation and solve for
:
Then we get two critical points,
We get an absolute maximum of at the second point, and an absolute minimum of
at the first point.
Explanation:
To reflect over the y axis, we apply this rule
which says to flip the sign of the x term but keep the y coordinate the same.
So that means something like J(-2,5) becomes J ' (2, 5). The other points are handled in the same fashion and that leads us to choice (d). Points on the y axis will stay where they are.