The temperature at a point in a room is given by T(x,y, z) = 200e-z²-3y²-9;2 where T is measured in C° and x, y, z are measured in meters. You are currently at the point (2, –1, 2). (a) Find the rate of change of the temperature in the direction (1, –4, 1). (b) What direction should you go to warm up the fastest? (c) What is the maximum rate of temperature increase?

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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(2) The temperature at a point in a room is given by
T(x, y, z) = 200e¬²²-3y²-9;²
where T is measured in C° and x, y, z are measured in meters. You are currently at the point (2, –1, 2).
(a) Find the rate of change of the temperature in the direction (1, –4, 1).
(b) What direction should you go to warm up the fastest?
(c) What is the maximum rate of temperature increase?
Transcribed Image Text:(2) The temperature at a point in a room is given by T(x, y, z) = 200e¬²²-3y²-9;² where T is measured in C° and x, y, z are measured in meters. You are currently at the point (2, –1, 2). (a) Find the rate of change of the temperature in the direction (1, –4, 1). (b) What direction should you go to warm up the fastest? (c) What is the maximum rate of temperature increase?
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