If the base variable is the number of units sold (or equivalently the difference in unit sales between the two) then the rate at which the deficit in/decreases is the first derivative, and the relative change in that rate is then the second derivative.
This is just about meaningful to non-maths people, because you can make the analogy with acceleration, but the third derivative? Reagan really was a joker. We think Dubya is the worst they've ever had, but we forget there've been others like him. Maybe not quite so utterly gormless in appearance but still.
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Derivatives
If the base variable is the number of units sold (or equivalently the difference in unit sales between the two) then the rate at which the deficit in/decreases is the first derivative, and the relative change in that rate is then the second derivative.
This is just about meaningful to non-maths people, because you can make the analogy with acceleration, but the third derivative? Reagan really was a joker. We think Dubya is the worst they've ever had, but we forget there've been others like him. Maybe not quite so utterly gormless in appearance but still.
Just my \frac{d}{dp} (p^2) worth.