The temperature at a point (x, y, z) is given by T(x, y, z) = (x + y)² + (y + 2)² + (x + 2)² where Tis measured in degree Celsius and x, y, z in meters. a. Find the direction the temperature decreases the fastest at P(1,6, -3). Write the answer in component form. b. Find the maximum rate of decrease at P(1,6, -3). Give the answer in exact form (i.e., a number or equivalent expression). c. Compute the directional derivative of T at P(1, 6, -3) in the direction of the vector v=-2i+3j5k. Give the exact answer.
The temperature at a point (x, y, z) is given by T(x, y, z) = (x + y)² + (y + 2)² + (x + 2)² where Tis measured in degree Celsius and x, y, z in meters. a. Find the direction the temperature decreases the fastest at P(1,6, -3). Write the answer in component form. b. Find the maximum rate of decrease at P(1,6, -3). Give the answer in exact form (i.e., a number or equivalent expression). c. Compute the directional derivative of T at P(1, 6, -3) in the direction of the vector v=-2i+3j5k. Give the exact answer.
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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Transcribed Image Text:The temperature at a point (x, y, z) is given by T(x, y, z) = (x + y)² + (y + 2)² + (x + 2)² where Tis
measured in degree Celsius and x, y, z in meters.
a. Find the direction the temperature decreases the fastest at P(1, 6, -3). Write the answer in
component form.
b. Find the maximum rate of decrease at P(1, 6, -3). Give the answer in exact form (i.e., a number
or equivalent expression).
c. Compute the directional derivative of T at P(1, 6, -3) in the direction of the vector
v = -2i+3j - 5k. Give the exact answer.
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