Main content

# Unit 5: Analyzing functions

1,800 possible mastery points

Mastered

Proficient

Familiar

Attempted

Not started

Quiz

Unit test

## About this unit

The first and the second derivative of a function can be used to obtain a lot of information about the behavior of that function. For example, the first derivative tells us where a function increases or decreases and where it has maximum or minimum points; the second derivative tells us where a function is concave up or down and where it has inflection points.

### 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!

### Learn

### Practice

- Find critical pointsGet 3 of 4 questions to level up!

### Learn

### Practice

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

### 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 560 Mastery points

### Learn

### Practice

- Concavity introGet 3 of 4 questions to level up!
- Inflection points introGet 3 of 4 questions to level up!

### Learn

### Practice

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

### Practice

- Second derivative testGet 3 of 4 questions to level up!

### 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 640 Mastery points

### Learn

### Practice

- OptimizationGet 3 of 4 questions to level up!

### Practice

- Tangents to graphs of implicit relationsGet 3 of 4 questions to level up!

### 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 1,800 Mastery points!