Please help answer the following questions regarding contour maps. You may include a sketch of a contour map and point(s) to help illustrate your points if you want.

a) What is a contour map?

b) How could we use a contour map to approximate a partial derivative? In your description you may assume the point itself is on a contour line.

c) Given a contour map and a point P on one of the contour lines, which direction would the gradient vector be pointing? Explain why (this does not need to be a proof, just the idea).