1. Stewart, Section 12.6, Exercises 24, 25, 28, 30, 32, 37, 57.
2. Prove that if f(x,y,z) = g(r), where r is the distance of the point
(x,y,z) from the origin, then
gradient(f) = g'(r)/r (x i + y j + z k)
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3. Stewart, Section 12.7, Exercises 6, 27, 50.
4. Identify and determine the nature of the critical points of the
function f(x,y,z) = x^3 + x z^2 - 3 x^2 + y^2 + 2 z^2