April 4, 1996      Math 311,        Quiz 9 


You are in a space ship traveling from the Earth
(coordinates (0,0,0)) to the point with coordinates (2,4,8) along the
curve Gamma(t)=(t,t^2,t^3). As you are traveling along this path
you pass through a radiation field, and at each point the amount of
Roentgens per minute is given by the function 

f(x,y,z) = 5 + sin(x) + y + z^2. 

What is the largest dosage of radiation you will experience?

Let f(x,y,z)=6x-8y+3z. Find the maximum and minimum values of
f subject to the constraint: x^2 + 2y^2 +3z^2 <= 1.



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