If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

# Unit: Applying derivatives to analyze functions

AP Calc:
FUN (BI)
,
FUN‑1 (EU)
,
FUN‑4 (EU)
Not feeling ready for this? Check out Get ready for AP® Calculus.

#### 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 160 Mastery 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)

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

#### Quiz 2

Level up on the above skills and collect up to 400 Mastery points

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

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)

AP Calc:
FUN (BI)
,
FUN‑4 (EU)
,
FUN‑4.A (LO)
,
FUN‑4.A.7 (EK)

## 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 400 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 240 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)

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)

## Calculator-active practice

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

### Learn

• No videos or articles available in this lesson

### Practice

#### Quiz 5

Level up on the above skills and collect up to 240 Mastery points
Up next for you:

#### Unit test

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

### About this unit

The first and the second derivative of a function give us all sorts of useful information about that function's behavior. The first derivative tells us where a function increases or decreases or has a maximum or minimum value; the second derivative tells us where a function is concave up or down and where it has inflection points.
AP® is a registered trademark of the College Board, which has not reviewed this resource.