Answer to Problem 18
has its largest value at B. (The
relative values of
are indicated by the lengths of the vectors drawn
above.) To understand why, think of the figure as a
sketch of level curves on a mountainside , and the
values of
as the altitude at the point
.
Now
at a point corresponds to the slope of the path in the
direction of steepest ascent. Clearly the climb is
steepest at B and least steep at C.