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.

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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