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December 16

Line chart shapes

Are there short names for chart curves that look like each of the four segments of a circle? Like how a chart shaped like the top-left of a circle would indicate that the rate of increase is slowing down, and a chart shaped like the top-right of a circle shows the rate of decrease increasing. All I can think of is "exponential growth" for the bottom-right of a circle, but that's not exactly right. Thank you. — Preceding unsigned comment added by 142.244.172.101 (talk) 22:46, 16 December 2012 (UTC)[reply]

Bottom right: increasing at an increasing rate.

Bottom left: decreasing at a decreasing absolute rate.

Top left: increasing at a decreasing rate.

Top right: decreasing at an increasing absolute rate.

Duoduoduo (talk) 23:09, 16 December 2012 (UTC)[reply]

I include the word absolute in the above since what is actually decreasing or increasing as you move to the right is not the first derivative, but the absolute value of the first derivative. Duoduoduo (talk) 19:16, 17 December 2012 (UTC)[reply]

And of course the extremes of the quarter-circles are tangents with either infinite or zero rate of change. Note that these shapes are definitely not exponential. -- SGBailey (talk) 16:57, 17 December 2012 (UTC)[reply]