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I need to say that a variable Y reaches its maximum value when X=1.

Is there any difference between saying "its value peaks at X=1" and saying "its value peaks for X=1"?

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    Why would you not just use when, exactly as you did in the question itself? Commented Aug 10, 2020 at 17:25

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This is a question of mathematical convention. You may use either construction. There is little or no difference in meaning.

In my own scientific experience, "...peaks for X=1" suggests (but only rather weakly) that X is a variable over which we may have some control, whereas "... peaks at X=1" suggests (again, only weakly) that the peaking is a matter of observation rather than control.

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