Der. App

• Explanation:

  • Notes | Annotated

  • Desmos

• Practice Problems:

  • Worksheet | Answers

• 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

• Explanation:

  • Notes | Annotated

• Practice Problems:

  • Worksheet

  • function: http://archives.math.utk.edu/visual.calculus/3/graphing.1/index.html

• Explanation:

  • Notes | Annotated

• Practice Problems:

  • • Using the graph of a function for first & second derivative WS | Answer

  • Function description given the derivative WS

  • Using Average Rate of Change WS

• Explanation:

  • Notes

• Practice Problems:

  • Worksheet

• Explanation:

  • Notes

  • Videos:

    • Hollis: Extreme Values on intervals

    • Khan: Maximum and minimum values on an interval

  • Practice Problems:

  • Worksheet

• Notes

• Explanation

  • Notes

• Practice Problems:

  • • Worksheet | Answer

  • 2004 Q4

  • 2000 Q5

• Notes

• Graph f(x) and f ’(x) with the graphing calculator WS

  • Desmos Activity: Sketchy Derivatives

• Explanation:

  • Notes:

    • Interpreting f ’ and f ’’ using a graph Notes: Notes

      • Interpreting the Graph of the Derivative of a Function and Explain your reasoning: Notes | Annotated

  • 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:

      • Derivatives and Tangent Lines: (Java)

    • 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

      • Activity: relationship between f(x) and f'(x)

      • Activity: relationship between f(x), f '(x), and f ''(x)

  • 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

• Explanation:

  • Notes | Annotated

  • Videos:

    • Hollis: Curve Sketching

    • Kahn: Calculus: Graphing Using Derivatives : Graphing functions using derivatives

    • Khan: Graphing with Calculus

  • Practice Problems:

  • Curve Sketching WS

  • 2005 Q4 - parts b, c, and d

• 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

• Study these flash cards | Study calculus flash cards

• WS #1 | Answers

• WS #2

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

Derivative Application Cumulative Review WS | Answers