[Math] Use Lagrange Multipliers to find the absolute extrema

calculuslagrange multipliermultivariable-calculusoptimization

Use Lagrange Multipliers to find the absolute extrema (if any) of:

$f(x,y) = 4x^2 + 9y^2$; subject to $2x +3y = 6$.

Using Lagrange I end up with one point: $(\frac{3}{2}, 1)$

I'm just not sure how to show if that point is a max or a min?

Best Answer

Note that $2x +3y = 6$ describes a line. Choose any other point on that line, say $(0, 2)$, and plug it into your original function. Is the value larger or smaller than when you plug your solution point into the function?

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