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## Homework Statement

Use lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist.

f(x,y) = x+3y, x

^{2}+y

^{2}≤2

## Homework Equations

grad f = λ grad g

## The Attempt at a Solution

to find critical points in the interior region,

The partial derivative of f(x,y) with respect to x is 1.

The partial derivative of f(x,y) with respect to y is 3.

g(x,y) = the constraint = x

^{2}+y

^{2}≤2, to find critical points on the boundary x

^{2}+y

^{2}=2

The partial derivative of g(x,y) with respect to x is 2x.

The partial derivative of g(x,y) with respect to y is 2y.

And normally I would set:

1 = λ 2x and 3 = λ 2y

λ = 1/2x and λ = 3/2y

so then I would set the equations equal to each other and solve the equation for x and y.

What I'm wondering though, Is whether there are actually minimum or maximum values since the partial derivatives of f(x,y) are constants?