Answer the Question. -You Are Hiking on a Mountainside, Following a Trail That

Multiple Choice

Answer the question.
-You are hiking on a mountainside, following a trail that slopes downward for a short distance and then begins to climb again. At the bottom of this local "dip", what can be said about the relationship between the trail's
Direction and the contour of the mountainside? [Hint - Think of the trail as a constrained path, g(x, y) = c, on the Mountainside's surface, altitude = f(x, y) . Consider only infinitesimal displacements.]

A) At the bottom of the dip, the trail is headed in the direction of the mountain's steepest ascent.
B) At the bottom of the dip, the trail is headed along the mountain's contour line which passes through that point.
C) The mountainside rises in all directions relative to the dip.
D) At the bottom of the dip, the trail is headed perpendicular to the mountain's contour line which passes through that point.