The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Courses » ap-calculus

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: [ap-calculus] Natural Log Derivative
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
James Hus

Posts: 20
Registered: 11/18/10
[ap-calculus] Natural Log Derivative
Posted: Nov 18, 2011 7:42 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Good problems spur good discussions.

1973 AB 23 lim h->0 (1/h)(ln( (2+h)/2 ) provides such discussion.

We have started to call some of these problems "stealth" problems because some of the parts are missing or don't appear in function form i.e. the ln (2/2) in this case.

We got past the preliminary questions of "What does this limit represent...etc"

The part of this functions slope that the students found interesting is the way to look at the transformations that can occur with or without using log properties. The slope of f(x) = ln (x/2) has the same slopes as g(x) = ln (x) or h(x) = ln (ax) (a=0). When using log properties they saw the family of functions that were shifted vertically. With no log properties they discussed the relationship to the curves with stretches/compression in the x direction.

I would love to hear about other favorite DQ problems (definition of a derivative) as well.

Course related websites:
To search the list archives for previous posts go to
To unsubscribe click here:
To change your subscription address or other settings click here:

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.