Multi-Variable Calculus Assignment

due Tuesday, March 6, 2001

Exercises

1. Let f be the function defined in R^{2} by

f(x, y) = x^{2} − xy + y^{2} − x + 3 ,

and let (u, v) be a given unit vector in R^{2}. Find the following:

(a) A formula for the directional derivative of f at the point (1, −2) in the direction of (u, v).

(b) The maximum value of the various directional derivatives of f at the point (1, −2).

2. Find a parametric representation for the line tangent at the point (2, 1, −2) to the piece of

curve that is the intersection of the surface

xy − z^{2} + 2 = 0

with the sphere

x^{2} + y^{2} + z^{2} = 9 .

[Processed from GELLMU to L^{A}TEX on Fri 2 Mar 2001 at 10:52:13 EST]