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

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

Af

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?

BL

WB

William B

0

1 spot left!

Af

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?

BL

WB

William B

0

1 spot left!

Af

Calculus · series session

#### Applying derivatives to analyze functions

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

SL

LG

Luca G

0

12/200

Af

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?

BL

WB

William B

0

7/50

Af

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?

BL

WB

William B

0

7/50

### That's it for now!

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