Sec. 4.5

#2a) grad(f) = (2x, 6y), so (0,0) is a critical point.

#2d) grad(f) = (-2x*exp(-x^2-y^2),-2y*exp(-x^2-y^2)), so (0,0) is a critical point.

#2e) grad(f) = (3x^2-y^2+y,-2xy+x). Critical points at (0,0) and (0,1).

Sec. 5.1

#1b) grad(f) = (2x+2y,2y+2x). Critical points are the set {(x,y) | x+y=0}.

#1c) grad(f) = (-2x*sin(x^2+y^2), -2y*sin(x^2+y^2)). Critical points are the set {all (x,y) so that x^2 + y^2 = k*pi where k = 0, 1, 2, 3, ...}

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Last modified: Mon Nov 4 16:44:48 1996