The temperature at a point (x, y, z) is given by T(x, y, z) = 1000-x²-542-782 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(4, -1, 3) in the direction toward the point (5, -5, 4). °C/m (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) = 1000-x²-542-782 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(4, -1, 3) in the direction toward the point (5, -5, 4). °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![The temperature at a point (x, y, z) is given by
T(x, y, z) = 1000-x²-542-782
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(4, -1, 3) in the direction toward the point (5, -5, 4).
°C/m
(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%2Fabb75337-a8ce-4ff9-8c07-7d58c277bdaa%2Fb1b9b73a-dcff-4dcc-90d6-7e25d38452bd%2F32qpdap_processed.png&w=3840&q=75)
Transcribed Image Text:The temperature at a point (x, y, z) is given by
T(x, y, z) = 1000-x²-542-782
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(4, -1, 3) in the direction toward the point (5, -5, 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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