Der. App
1) Function Description - increasing/decreasing/extrema
2) Function description - concavity & points of inflection
- Explanation:
- Notes | Annotated
- Video:
- Hollis: Concavity: slides 1 and 3-4
- Khan: Inflection Points and Concavity Intuition
- Video: Hollis: Second derivative test - slide 5-9
3) Function Description (domain is not all real numbers)
- Explanation:
- Notes | Annotated
- Practice Problems:
4) Function description given the derivative
- Explanation:
- Practice Problems:
5) Local extrema on open or closed intervals
6) Absolute Extrema and Extreme Value Theorem
7) Absolute Extrema on an open interval or the entire domain of a function
8) Application of Implicit Differentiation
Vocabulary Review
Study these flash cards | Study calculus flash cards
9) Graph f(x) and f ’(x) with the graphing calculator
10) Interpreting the first and second derivative on a number line and coordinate plane graph
- Explanation:
- Notes:
- Video:
- Hollis: The derivative (slides #5-7, and 10) - 20 min. video (cumulative - definition, shortcuts with rules, and applications)
- Websites: Mapping the slope of a function to the y-values ("height") of the derivative curve:
- Any function:
- Specific functions
- Sliders adjust the function and its derivative on Desmos
- Cubic function | (Java)
- Fourth Power (Java)
- Sine curve (Quicktime)
- Practice Problems:
- Interpreting f ’ Number Line or Graph WS | Answers
- Interpret the graph of the derivative & Explain your Reasoning WS
- The numerical value of the slope of the tangent lines become the y-values of the derivative: Khan Module: video explanation | Derivative Intuition
- Matching graphs of f, f ' and f '' (website - Java):
- Desmos Activity: Functions and Their Derivatives
- Desmos Activity: Card Sort: Derivative Match
- Applets: Derivative puzzles 1 - 3 are matching games with function, derivative and second derivative graph; arrange the graphs in columns with the function at the top, its derivative below it and the second derivative on the bottom.
- Applet: First and second derivative has a slider for a coefficient of third order polynomial. As the coefficients changes, you can observe the changes in the graph of the function and the graph of the derivative
- 2010 Q5 - parts b and c
- 2009 (Form B) Q5
- 2009 Q6 - parts a and c
- 2007 (Form B) Q4 - parts a, b, and c
- 2004 (Form B) Q4 - parts a and c
- 2003 Q4 - parts a, b and c
- 2000 Q3
11) Curve Sketching by Hand
- Explanation:
- Notes | Annotated
- Videos:
- Practice Problems:
- Curve Sketching WS
- 2005 Q4 - parts b, c, and d
12) Mean Value Theorem (MVT)
- Explanation:
- Notes | Annotated
- Khan video: Mean Value Theorem
- Interactive - mean value theorem
- College Board: Weakening the Hypotheses of the Mean Value Theorem
- Practice Problems:
- 2009 (Form B) Q3
- 2008 (Form B) Q5 - parts a, c, and d
13) Derivative Application Review
Critical thinking quiz: http://archives.math.utk.edu/visual.calculus/3/graphing.2/index.html
AP Free Response Questions
- 2011 (Form B) Q4 - max/min, concavity - parts a and b
- 2010 (Form B) Q2 - tangent line and concavity - part a, b, and d
- 2008 Q6 - tangent line, max/min, limit
- 2007 (Form B) Q6 - existence theorems, chain rule
- 2007 Q6 - derivatives, max/min, inflection point
- 2007 Q3 - existence theorems, chain rule, derivative of inverse functions
- 2004 Q4 - Implicit differentiation & max/min
- 2001 Q4 - max/min, concavity, tangent line
- 1999 Q4 - tangent point, inflection point, max/min
- 1998 Q2 - limit as x approaches infinity, max/min