The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-²-S2-922 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature (in "C/m) at the point P(2, -1, 3) in the direction toward the point (5, -3, 4). C/m

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)= 100e-²-Sy2 - 922
where T is measured in °C and x, y, z in meters.
(a) Find the rate of change of temperature (in °C/m) at the point P(2, -1, 3) in the direction toward the point (5, -3, 4).
C/m
(b) In which direction does the temperature increase fastest at P?
(c) Find the maximum rate of increase at P.
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Transcribed Image Text:The temperature at a point (x, y, z) is given by T(x, y, z)= 100e-²-Sy2 - 922 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature (in °C/m) at the point P(2, -1, 3) in the direction toward the point (5, -3, 4). C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P. Need Help? Read It
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