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Math 250 Midterm #3. November 12, 2004
Attention! Please, note that this is the closed book test. You are not allowed to use graphing
calculator. Simple calculators are allowed. Please, show all important steps in you solution but do
not make your solution excessively long.
1. (15pt) Find all stationary points of the function
f(x) = e2x
(x + y2
+ 2y).
2
2. (20pt) Write Lagrange's equations, DO NOT SOLVE, for the problem of find
ing the extremuma of the function:
f(x, y, z) = xyz,
subject to constraint equaitons
x + y + z = 5
xy + xz + yz = 8
Midterm 3. Name: ID: 3
