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ExploreCalculusApplying derivatives to analyze functions

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Calculus

Applying derivatives to analyze functions

  • Using the mean value theorem
  • Extreme value theorem, global versus local extrema, and critical points
  • Determining intervals on which a function is increasing or decreasing
  • Using the first derivative test to find relative (local) extrema
  • Using the candidates test to find absolute (global) extrema
  • Determining concavity of intervals and finding points of inflection: graphical
  • Determining concavity of intervals and finding points of inflection: algebraic
  • Using the second derivative test to find extrema
  • Sketching curves of functions and their derivatives
  • Connecting a function, its first derivative, and its second derivative
  • Solving optimization problems
  • Exploring behaviors of implicit relations
  • Calculator-active practice

Small-group help sessions in "Applying derivatives to analyze functions"

Register for a session to review this topic with a small group of learners.

Calculus · series session

Applying derivatives to analyze functions

5.1 - What is the MVT?
5.2 - What is the EVT?
5.3 - How can we use derivatives to determine intervals where a function is increasing/decreasing?
5.4 - How can we use the first derivative to find local maxes and mins?
5.5 - What’s different with the candidates' test?

William B

0
1 spot left!

Calculus · series session

Applying derivatives to analyze functions

5.6 - What is concavity? How can we determine concavity across an interval?
5.7 - How can we use a second derivative to find local maxes and mins?
5.8 - Can you sketch the relative graph of a function if given a derivative?
5.9 - What’s important about:
The first derivative?
The second derivative?
5.10 and 5.11 - How can we optimize a value in a certain situation?
5.12 - What’s a critical point?

William B

0
1 spot left!

Calculus · series session

Applying derivatives to analyze functions

Theorems, maxima, minima, concavity, and increasing/decreasing behavior of a function through its derivatives!

Luca G

0
12/200

Calculus · series session

Applying derivatives to analyze functions

5.1 - What is the MVT?
5.2 - What is the EVT?
5.3 - How can we use derivatives to determine intervals where a function is increasing/decreasing?
5.4 - How can we use the first derivative to find local maxes and mins?
5.5 - What’s different with the candidates test?

William B

0
7/50

Calculus · series session

Applying derivatives to analyze functions

5.6 - What is concavity? How can we determine concavity across an interval?
5.7 - How can we use a second derivative to find local maxes and mins?
5.8 - Can you sketch the relative graph of a function if given a derivative?
5.9 - What’s important about:
The first derivative?
The second derivative?
5.10 and 5.11 - How can we optimize a value in a certain situation?
5.12 - What’s a critical point?

William B

0
7/50

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