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©¢ ¦ ¥¢ ¦ 2.(1 pt) The function f x y z
x4 y3 y2 z2 z5 x2 4x
4y 3z increases most rapidly at the point P 1 1 1 in the direction
i
j
k.
The rate of increase at P in this direction is
.
The rate of increase at P in the direction of the point Q 3 2 6
is
.
The equation of the tangent plane to the level surface f x y z
14 is
x1
y1
z1
0.
x
3.(1 pt) Suppose f x y
4 4 and v 2i j.
,P
y
A. Find the gradient of f .
∇f
i
j
Note: Your answers should be expressions of x and y; e.g.
“3x 4y”.
B. Find the gradient of f at the point P.
∇f P
i
j
Note: Your answers should be numbers.
C. Find the directional derivative of f at P in the direction of
the displacement vector...
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This note was uploaded on 11/09/2011 for the course MATH 262 taught by Professor Faber during the Spring '08 term at McGill.
 Spring '08
 FABER

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