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[See Solution] (a) Find the highest and lowest points on the ellipse of intersection of the cylinder x^2+y^2=1 and the plane x+y+z=1 (b) Find all minimum and

Question: (a) Find the highest and lowest points on the ellipse of intersection of the cylinder $x^{2}+y^{2}=1$ and the plane $x+y+z=1$

(b) Find all minimum and maximum points of the function

\[u(x, y, z)=x y z\]

on the circle in $\mathbb{R}^{3}$ formed as intersection of the plane

\[x+y+z=1\]

and the sphere of radius 1

\[x^{2}+y^{2}+z^{2}=1\]

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Solution: The downloadable solution consists of 4 pages
Deliverable: Word Document

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[See Solution] (a) Find the highest and lowest points on the ellipse of intersection of the cylinder x^2+y^2=1 and the plane x+y+z=1 (b) Find all minimum and

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