Mainly the concept that derivative equals rate of change. The example of taking average velocity over a minute, half a minute, a tenth of a minute, et cetera, is a little cliche, but I think it's the best way to give people a sense of what instantaneous velocity (and thus the derivative) means.
Depending on how short you're talking about, I think it's good to show a derivative calculation using the definition (of, say, 5x^2+3x) and then explain the power rule; that conveys the idea that calculus takes these complex calculations and compresses them into quick conversions.
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Date: 2009-09-04 04:08 am (UTC)Depending on how short you're talking about, I think it's good to show a derivative calculation using the definition (of, say, 5x^2+3x) and then explain the power rule; that conveys the idea that calculus takes these complex calculations and compresses them into quick conversions.