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

### 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 Calc:

FUN (BI)

, FUN‑1 (EU)

, FUN‑1.B (LO)

, FUN‑1.B.1 (EK)

### Learn

### Practice

- Using the mean value theoremGet 3 of 4 questions to level up!
- Justification with the mean value theoremGet 3 of 4 questions to level up!

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)

### Learn

### 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)

### Learn

### Practice

- Relative minima & maximaGet 3 of 4 questions to level up!

AP Calc:

FUN (BI)

, FUN‑4 (EU)

, FUN‑4.A (LO)

, FUN‑4.A.3 (EK)

### Learn

### 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!

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)

### Learn

### 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)

### Learn

### Practice

- Analyze concavityGet 3 of 4 questions to level up!
- Find inflection pointsGet 3 of 4 questions to level up!

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!

AP Calc:

FUN (BI)

, FUN‑4 (EU)

, FUN‑4.A (LO)

, FUN‑4.A.10 (EK)

, FUN‑4.A.9 (EK)

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.10 (EK)

, FUN‑4.A.11 (EK)

### Learn

### Practice

- Justification using first derivativeGet 3 of 4 questions to level up!
- Justification using second derivativeGet 3 of 4 questions to level up!
- Connecting f, f', and f'' graphicallyGet 3 of 4 questions to level up!

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)

### Learn

### Practice

- OptimizationGet 3 of 4 questions to level up!

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!

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!

Level up on the above skills and collect up to 240 Mastery points

Up next for you:

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

AP® is a registered trademark of the College Board, which has not reviewed this resource.