near this trial solution. This is done by evaluating the partial derivatives
at (0, 0):
.
subject to the original constraints yields the solution
with 
.
However since (2, 1) is not near
(0, 0) the approximation may not be a good one at (2, 1). [Note that
is well under .]
Rather than just accepting (2, 1) as the next trial solution , let us check
the line segment between (0, 0) and (2, 1) and choose the
with the largest .