Raptors Quiz

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Math 241 Fall 2011
Quiz 2
READ: (Inspired by http://www.xkcd.com/135) You are stranded hanging from a tree in the
jungle on the side of a steep hill given by the equation g(x, y, z) = x + y - z = 0. Your location
is 18 feet above the origin (i.e. at the point (0, 0, 18)).
Unfortunately this jungle you are in is infested with savage velociraptors who know how to use
Lagrange multipliers when necessary. Show your work and circle your answers. Justify your
answers whenever possible. No calculators. Remember, raptors do not know fear.
1. (1 point) Give the formula for the distance squared d2 = f(x, y, z) between a raptor located
at point (x, y, z) and your position (0, 0, 18).
2. (1 point) Compute f and g ( denotes the gradient).
3. (3 points) Use Lagrange multipliers to find the point on the plane which is closest to you.
4. (0 points) (For fun.) What is the distance between you and this closest point? If raptors

can jump 12 feet into the air, will you be able to live? (You can use the fact that
3 < 2.)