From: Kevin Sharitz [mailto:email@example.com] 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:firstname.lastname@example.org]<mailto:[mailto:email@example.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 <firstname.lastname@example.org<mailto:email@example.com>> 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