The temperature at a point (x, y, z) is given by T(x, y, z) = 400e -x2 - 5y2 - 722 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, 2) in the direction toward the point (6, -4, 6). °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) = 400e -x2 - 5y2 - 722 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, 2) in the direction toward the point (6, -4, 6). °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...

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Question

What are the specific functions that I use? and how do I solve in steps so I can reference for futue problems?

The temperature at a point (x, y, z) is given by
Т(x, у, 2)
400e-x2 - 5y2 - 722
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, 2) in the direction toward the point (6, -4, 6).
°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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