Date: Oct 26, 2012 11:44 AM
Author: Barbara De Roes
Subject: [ap-calculus] one-sided derivatives
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I'm curious how common is it for your students to make the following mistake:

suppose g(x) is defined in 2 pieces, and is not continuous at the break, such as

x+1 for x>2

x-3 for x<=2

when asked to evaluate g' from each side at 2, the student uses the value of the PIECE for g(2), namely g(2) = -1 from the left, but g(2) magically becomes 3 from the right.

I'm wondering if this is just one of those developmental things where the brain does a reset of prior knowledge, or if my precalc curriculum is unusually weak in this regard.

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