The temperature at the point (x, y) on a metal plate is given by the function2T(x, y) = 2 - 4x² - y² + xy.Find the direction of greatest increase in heat from the point (1, 1) and the rate of increase.

Given , T(x,y) = 2 - 4x2 - y2 + xyHeat flow at the Point (1,1)

Answered: The temperature at the point (x, y) on…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The temperature at the point (x, y) on a metal plate is given by the function T(x, y) = 2 - 4x² - y² + xy. Find the direction of greatest increase in heat from the point (1, 1) and the rate of increase.