The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x2 - Sy2 - 722 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 2) in the direction towards the point (6, -5, 4). -49 -2100e °C/m (b) In which direction does the temperature increase fastest at P? xi + 5yj + 7zk) (c) Find the maximum rate of increase at P. -18 1.617.10

The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x2 - Sy2 - 722 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 2) in the direction towards the point (6, -5, 4). -49 -2100e °C/m (b) In which direction does the temperature increase fastest at P? xi + 5yj + 7zk) (c) Find the maximum rate of increase at P. -18 1.617.10

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.3: Rates Of Change

Problem 29E: Explain the difference between the average rate of change of y as x changes a to b, and the...

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