Teaching Concavity

As you’ve probably noticed, different authors use different definitions based on how they plan to present topics later in their texts. So, the same concept seems to have different definitions. A definition in one book is a theorem in another. Students should be aware of this; looking at different definitions and related theorems about the…

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L’Hospital’s Rule

Another application of the derivative L’Hospital’s Rule  Locally Linear L’Hospital’s Demonstration of the proof L’Hospital Rules the Graph Good Question An AP Exam question that can be used to delve deeper into L’Hospital’s Rule (2008 AB 6) Revised from a post of November 7, 2017 There will be two extra posts this week! Check tomorrow for some…

On Scaling

Why “scaling” is necessary No teacher can make two tests on the same topics equal in difficulty. No two teachers, even if they collaborate, can make two tests on the same topic equal in difficulty. No two teachers in different schools, districts, or states can make two tests on the same subject equal in difficulty.…

On Grading

I got to thinking about grading the other day after seeing a question on Facebook. We’ll get to that question in a minute, but first I want to try to outline a grading scheme I used towards the end of my teaching career. It is based on how free-response question on AP Calculus exams are…

Inverses

This series of posts reviews and expands what students know from pre-calculus about inverses. This leads to finding the derivative of exponential functions, ax, and the definition of e, from which comes the definition of the natural logarithm. Inverses Graphically and Numerically The Range of the Inverse The Calculus of Inverses The Derivatives of Exponential Functions…