The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x² - 3y2 - 9z2 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, 4) in the direction towards the point (5, –4, 5). °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) = 100e-x² - 3y2 - 9z2 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, 4) in the direction towards the point (5, –4, 5). °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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![The temperature at a point (x, y, z) is given by
T(x, y, z) = 100e-x2 - 3y2 – 9z2
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, 4) in the direction towards the point (5, -4, 5).
°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%2F25fce74d-50ce-4010-8593-c528dce466b9%2F9438a2aa-309d-4a8c-b3d2-2f4702bb1bcc%2Fxg15zfj_processed.png&w=3840&q=75)
Transcribed Image Text:The temperature at a point (x, y, z) is given by
T(x, y, z) = 100e-x2 - 3y2 – 9z2
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, 4) in the direction towards the point (5, -4, 5).
°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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