MATH 251
Section 14-8
1. Find the extreme values of the functions 𝑓(𝑥, 𝑦) = 𝑥 2 + 2𝑦 2 on the circle 𝑥 2 + 𝑦 2 = 1.
2. Find extreme values of the function 𝑓(𝑥, 𝑦, 𝑧) subject to the given constant 𝑔(𝑥, 𝑦, 𝑧) where
3. Find the points on the sphere 𝑥 2 + 𝑦 2 + 𝑧 2 = 4 that are closest to and farthest from the point
(3,1, −1).
4. Find the extreme values of 𝑓(𝑥, 𝑦) on the elliptical region 4𝑥 2 + 𝑦 2 ≤ 1 where 𝑓(𝑥, 𝑦) =
𝑒 −2𝑥𝑦
5. Find the volume of the largest rectangular box in the first octant with three faces in the coordinate
planes and one vertex in the plane 𝑥 + 2𝑦 + 3𝑧 = 6.