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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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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.
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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