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First and Second Derivative Test

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Agenda

  • Graphing Review
  • Concavity and Second Derivative Test
  • Desmos Activity
  • Practice

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Graphing Review

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Steps for Graphing

  • Domain
  • Intercepts
  • Asymptotes
  • First Derivative
  • Graph
  • Range

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  • Now we will add concavity and the second derivative test

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Concavity

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Concavity

  • Concavity is a measure of the curvature of a function
  • Concavity is the change in the first derivative
    • Is the first derivative increasing or decreasing
  • How much does the first derivative change?
    • Find this through the second derivative!
  • See Jamboard A4 Examples First and Second Derivative Test

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Second Derivative Test

  • If a critical point (where derivative is zero) has second derivative positive
    • Then extrema is minimum
  • If a critical point has second derivative negative
    • Then extrema is maximum
  • This is the second derivative test
    • Make a table like 1st deriv test and asymptote chart

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Inflection Points

  • Inflection points are where the concavity changes sign
  • Concave up to down or concave down to up
  • Set second derivative to zero then solve
  • Can use a table to help determine concavity of the function (up or down)

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Desmos Activity

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Desmos Activity

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Practice

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Practice

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CREDITS

Special thanks to all the people who made and released these awesome resources for free:

  • Presentation template by SlidesCarnival

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