The temperature at a point (x, y, z) is given by T(x, y, z) = 400e-x² - 5y² - 922 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(2, -1, 3) in the direction towards the point (4, -2, 5). °C/m X (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.
The temperature at a point (x, y, z) is given by T(x, y, z) = 400e-x² - 5y² - 922 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(2, -1, 3) in the direction towards the point (4, -2, 5). °C/m X (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.3: Rates Of Change
Problem 29E: Explain the difference between the average rate of change of y as x changes a to b, and the...
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![The temperature at a point (x, y, z) is given by
T(x, y, z) = 400e-x² - 5y² - 922
where T is measured in °C and x, y, z in meters.
(a) Find the rate of change of temperature at the point P(2, -1, 3) in the direction towards the point (4, -2, 5).
°C/m
X
(b) In which direction does the temperature increase fastest at P?
(c) Find the maximum rate of increase at P.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd20c9d63-395d-4692-a314-612694e3f8ce%2F880bf4ae-880d-415c-997b-b3bebeba401d%2Fq5yqlke_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The temperature at a point (x, y, z) is given by
T(x, y, z) = 400e-x² - 5y² - 922
where T is measured in °C and x, y, z in meters.
(a) Find the rate of change of temperature at the point P(2, -1, 3) in the direction towards the point (4, -2, 5).
°C/m
X
(b) In which direction does the temperature increase fastest at P?
(c) Find the maximum rate of increase at P.
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