and for use the points (-6,18.2,158) and (-6,14,159), and
, and
.
Using the tangent plane to estimate f(-7,15) yields an approximate value
of z=163.04 which compared to the actual value of f(-7,15)=160.45 gives
a relative error of . A relative error of 1.6% is a good approximation.
so,
Since this is greater than 0.05, we must move one unit in the direction of from the point (-6.99,14.01). The unit vector in
the direction of
is
, so we should move one
unit in the positive y direction to the point (-6.99,15.01). The
gradient at this point is
The difference in the magnitudes of the gradients from (-6.99,14.01) and (-6.99,15.01) is
which is less than 0.05, so we can stop.