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In optimisation, does First Order Condition (FOC) always mean a condition for a max/min related to the first derivative.

Similarly, is Second Order Condition (SOC), called second order because it relates to the second derivative?

Assuming this is correct, when I see FOC or SOC in economics can I generally assume they are referring to some kind of condition on the first and second derivatives respectively, to ensure a max/min?

Is there any other use of the terms "[number] Order Condition," that isn't referring to the derivatives. Or more broadly isn't referring to optimisation.

This may seem simple, but weirdly when I first learnt this, I more just associated the conditions with actual order and a sense of rigourousness. I.e. the FOC was the first thing we did, and then the SOC was the second thing we did, and it felt a bit more strict. Rather than associating it explicitly with derivatives.

Thanks!

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Yes, this is terminology borrowed from mathematics. First order conditions relate to derivative of first order and second order conditions to derivative of second order. It has nothing to do with which one you do first.

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