An application of the Tangent Plane

Question 6

You live in a town in southern California recently experiencing drastic floods. The rains are coming and you are starting to panic, you must find high ground now! You can describe the land you live on with the function f(x,y)=-(x-2)^2-y^2-y

What is the safest place for you to be as the rain falls down (Place where you will survive the longest)? What does this have to do with the tangent plane and the partial derivatives? Can you generalize your answer to finding "safest spots" for any f(x,y) using the tangent plane and the partial derivatives?

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