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# Unit: Applying derivatives to analyze functions

AP Calc:
FUN (BI)
,
FUN‑1 (EU)
,
FUN‑4 (EU)

#### 0

Possible mastery points

## Using the mean value theorem

AP Calc:
FUN (BI)
,
FUN‑1 (EU)
,
FUN‑1.B (LO)
,
FUN‑1.B.1 (EK)

#### Quiz 1

Level up on the above skills and collect up to 200 Mastery points

## Extreme value theorem, global versus local extrema, and critical points

AP Calc:
FUN (BI)
,
FUN‑1 (EU)
,
FUN‑1.C (LO)
,
FUN‑1.C.1 (EK)
,
FUN‑1.C.2 (EK)
,
FUN‑1.C.3 (EK)
Practice
Find critical pointsGet 3 of 4 questions to level up!

AP Calc:
FUN (BI)
,
FUN‑4 (EU)
,
FUN‑4.A (LO)
,
FUN‑4.A.1 (EK)

AP Calc:
FUN (BI)
,
FUN‑4 (EU)
,
FUN‑4.A (LO)
,
FUN‑4.A.2 (EK)

## Using the candidates test to find absolute (global) extrema

AP Calc:
FUN (BI)
,
FUN‑4 (EU)
,
FUN‑4.A (LO)
,
FUN‑4.A.3 (EK)
Practice
Absolute minima & maxima (closed intervals)Get 3 of 4 questions to level up!
Absolute minima & maxima (entire domain)Get 3 of 4 questions to level up!

#### Quiz 2

Level up on the above skills and collect up to 500 Mastery points

## Determining concavity of intervals and finding points of inflection: graphical

AP Calc:
FUN (BI)
,
FUN‑4 (EU)
,
FUN‑4.A (LO)
,
FUN‑4.A.4 (EK)
,
FUN‑4.A.5 (EK)
Practice
Concavity introGet 3 of 4 questions to level up!
Inflection points introGet 3 of 4 questions to level up!

AP Calc:
FUN (BI)
,
FUN‑4 (EU)
,
FUN‑4.A (LO)
,
FUN‑4.A.4 (EK)
,
FUN‑4.A.5 (EK)
,
FUN‑4.A.6 (EK)

## Using the second derivative test to find extrema

AP Calc:
FUN (BI)
,
FUN‑4 (EU)
,
FUN‑4.A (LO)
,
FUN‑4.A.7 (EK)
Practice
Second derivative testGet 3 of 4 questions to level up!

## Sketching curves of functions and their derivatives

AP Calc:
FUN (BI)
,
FUN‑4 (EU)
,
FUN‑4.A (LO)
,
FUN‑4.A.10 (EK)
,
FUN‑4.A.9 (EK)

#### Quiz 3

Level up on the above skills and collect up to 500 Mastery points

## Connecting a function, its first derivative, and its second derivative

AP Calc:
FUN (BI)
,
FUN‑4 (EU)
,
FUN‑4.A (LO)
,
FUN‑4.A.10 (EK)
,
FUN‑4.A.11 (EK)

#### Quiz 4

Level up on the above skills and collect up to 300 Mastery points

AP Calc:
FUN (BI)
,
FUN‑4 (EU)
,
FUN‑4.B (LO)
,
FUN‑4.B.1 (EK)
,
FUN‑4.C (LO)
,
FUN‑4.C.1 (EK)

## Exploring behaviors of implicit relations

AP Calc:
FUN (BI)
,
FUN‑4 (EU)
,
FUN‑4.D (LO)
,
FUN‑4.D.1 (EK)
,
FUN‑4.E (LO)
,
FUN‑4.E.1 (EK)
,
FUN‑4.E.2 (EK)
Practice
Tangents to graphs of implicit relationsGet 3 of 4 questions to level up!

## Calculator-active practice

AP Calc:
FUN (BI)
,
FUN‑4 (EU)
,
FUN‑4.A (LO)
Learn
No videos or articles available in this lesson
Practice
Analyze functions (calculator-active)Get 3 of 4 questions to level up!

#### Quiz 5

Level up on the above skills and collect up to 300 Mastery points
Up next for you:

#### Unit test

Level up on all the skills in this unit and collect up to 1800 Mastery points!