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.
For this case we have by definition, that the equation of a line in the slope-intersection form is given by:
Where:
m: It is the slope of the line
b: It is the cut point with the "y" axis
We have, according to the data provided, that the line is of the form:
That means that the slope is -1.
ANswer: