The temperature at a point (x, y, z) is given by -x² - sy² - 722 T(x, y, z) = 100e 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, 4) in the direction toward the point (5, -4, 5). 7400 -121 e °C/m V 19 (b) In which direction does the temperature increase fastest at P? -400e-121 1,200e -121 - 5600e 121 (c) Find the maximum rate of increase at P. 100/3156 e -121

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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The temperature at a point (x, y, z) is given by
,² - 5y² – 722
T(x, y, z) = 100e
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, 4) in the direction toward the point (5, -4, 5).
7400 -121
e
°C/m
V 19
(b) In
nich direction does the temperature increase fastest at P?
-121
-400e 121
1,200e
- 5600e-121
(c) Find the maximum rate of increase at P.
-121
100/3156 e
Transcribed Image Text:The temperature at a point (x, y, z) is given by ,² - 5y² – 722 T(x, y, z) = 100e 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, 4) in the direction toward the point (5, -4, 5). 7400 -121 e °C/m V 19 (b) In nich direction does the temperature increase fastest at P? -121 -400e 121 1,200e - 5600e-121 (c) Find the maximum rate of increase at P. -121 100/3156 e
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