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## Homework Statement

Find the minimum and maximum values of the function subject to the given constraint

f(x,y) = x^2 + y^2, 2x + 3y = 6

## Homework Equations

[itex]\nabla[/itex]f, [itex]\nabla[/itex]g

## The Attempt at a Solution

After doing all the calculation, x value and y value came out to be ([itex]\frac{12}{13}[/itex],[itex]\frac{18}{13}[/itex]). After plugging them into f(x,y), my answer came out as [itex]\frac{468}{169}[/itex]. I thought it was maximum. But when I checked the answer, it said it was minimum and maximum value doesn't exist. I thought if the value was positive, it was maximum and if negative, it was minimum, but apparently I am wrong. Would anyone tell me how to correctly determine if the value is maximum or minimum?

Thank you