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RE: [ap-calculus] alternate definition of derivative
Posted:
Sep 17, 2012 10:59 AM
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Thank you all so much for your responses. :)
Appended to this posting by the moderator:
This ap-calculus EDG will be closing in the next few weeks. Please sign up for the new AP Calculus Teacher Community Forum at https://apcommunity.collegeboard.org/getting-started and post messages there.
Lin McMullin
Calculus EDG Moderator
From: Kevin Sharitz [mailto:sharitzkevin@rockwood.k12.mo.us]
Sent: Saturday, September 15, 2012 5:22 PM
To: AP Calculus
Subject: RE: [ap-calculus] alternate definition of derivative
I agree. Factoring out a (-1) from numerator and denominator to take limx ->c (f(x)-f(c))/(x-c) and turn it into
limx ->c (-1)(f(c)-f(x))/(-1)(c-x) thus limx ->c (f(c)-f(x))/(c-x) is perfectly acceptable....not necessarily recommended due to AP tendency of giving limit
problems where students are expected to recognize the given limit is definition of derivative and use their derivative shortcuts to evaluate the limit. So I think this is another
one of those scenarios where you say, "Yes, you could do that. You could also do your derivatives with limits instead of using the shortcuts, but that doesnt mean you should".
From: Earley, Ned [Earley.Ned@lebanon.k12.oh.us]
Sent: Friday, September 14, 2012 1:34 PM
To: AP Calculus
Subject: RE: [ap-calculus] alternate definition of derivative
I disagree, I think it is equivalent.
Respectfully,
Ned Earley
From: Carole Stevens [mailto:cstevens@mkchs.com]<mailto:[mailto:cstevens@mkchs.com]>
Sent: Friday, September 14, 2012 2:14 PM
To: AP Calculus
Cc: AP Calculus
Subject: Re: [ap-calculus] alternate definition of derivative
It is not okay. c is not appoaching x; c is the location that the "movable" x is approaching, so even though "slope" is interchangeable, the limit was written incorrectly.
On Fri, Sep 14, 2012 at 8:11 AM, Kandice Tucker <ktucke@spartanburg3.org<mailto:ktucke@spartanburg3.org>> wrote:
I have a student ask if you can write the definition of derivative limxapproaches c of [f(c)-f(x)]/[c-x]. He used it this way and got the correct answer. He argued that the slope is interchangeable. He got the correct answer in the end. Is this ok? Thanks,
Kandice Tucker
Broome High School
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