MAT 228 Final: F08finalsol
31 Jan 2019
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Knightly: (12 pts) find the rate of change of the function f (x, y) = x2y + y3 at the point (2, 1) in the direction of the vector h 3, 4i. The gradient is f (x, y) = h2xy, x2 + 3y2i. Therefore the directional derivative is u = h 3, 4i k h 3, 4ik. Duf (2, 1) = f (2, 1) u = h4, 7i h 3/5, 4/5i = 12. 5: (14 pts) a plane contains the points p = (1, 0, 0), q = ( 1, 2, 4) and r = (3, 4, 0). (a) find the vectors ~p q and ~p r. ~p r = h2, 4, 0i . (b) find an equation for the plane. A normal vector is given by: n = ~p q ~p r = h 16, 8, 12i . (details of cross product omitted. ) For simplicity, let"s scale the above vector by 1/4, and rede ne.
