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6. Suppose that the temperature T at point (x, y,z) is given by the function T = 2x2 – y? + 4z², and that a tiny heat-loving bug, currently hovering at point (1, –2,1), wants to fly in the direction in which the temperature is increasing most rapidly. Find a vector pointing in the direction he should fly.

6. Suppose that the temperature T at point (x, y,z) is given by the function T = 2x2 – y? + 4z², and that a tiny heat-loving bug, currently hovering at point (1, –2,1), wants to fly in the direction in which the temperature is increasing most rapidly. Find a vector pointing in the direction he should fly.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. Suppose that the temperature T at point (x, y, z) is given by the function T = 2x? – y? + 4z², and that a tiny heat-loving bug, currently hovering at point (1, –2,1), wants to fly in the direction in which the temperature is increasing most rapidly. Find a vector pointing in the direction he should fly.
Transcribed Image Text:6. Suppose that the temperature T at point (x, y, z) is given by the function T = 2x? – y? + 4z², and that a tiny heat-loving bug, currently hovering at point (1, –2,1), wants to fly in the direction in which the temperature is increasing most rapidly. Find a vector pointing in the direction he should fly.
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