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## Homework Statement

The temperature at a point (x, y) on a metal plate is T(x, y) = 4x^2 − 4xy + y^2 .

An ant, walking on the plate, traverses a circle of radius 5 centered at the origin.

Using the method of Lagrange multipliers, find the highest and lowest

temperatures encountered by the ant.

## Homework Equations

## The Attempt at a Solution

T(x,y) = 4x^2 − 4xy + y^2

gradient of T = (8x - 4y)i + (2y - 4x)j

g(x,y) = x^2 + y^2 = 5^2

gradient of g = (2x)i + (2y)j

gradient of T = (lambda)gradient of g ----> lambda=#

8x - 4y = #2x ---->1

2y - 4x = #2y ---->2

# = 4-4y = 1-4x

what am i going to do next?