(6) Find the direction and magnitude of the greatest rate of change of T at (3 -) 2)

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The temperature is T degrees at any point (x, y, z)
in three-dimensional space and
T(x,y, z) = 1/(x² + y² + z² + 3).
Distance is measured in inches.
(a) Find the rate of change of the temperature at the point (3, –2, 2) in the
direction of the vector –2î+3 j-6 k.
(6) Find the direction and magnitude of the greatest rate of change of T at
(3, -2, 2).
Transcribed Image Text:The temperature is T degrees at any point (x, y, z) in three-dimensional space and T(x,y, z) = 1/(x² + y² + z² + 3). Distance is measured in inches. (a) Find the rate of change of the temperature at the point (3, –2, 2) in the direction of the vector –2î+3 j-6 k. (6) Find the direction and magnitude of the greatest rate of change of T at (3, -2, 2).
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