# Concavity and inflection points

5 videos
3 skills
One of the neat things about calculus is that it gives us a mathematical way to describe the shape of curves. In this tutorial, you will learn about concavity and inflection points, which describe quantitatively how a curve curves. This will be useful for finding maxima and minima.

### Concavity, concave upwards and concave downwards intervals

VIDEO 9:54 minutes
What is concavity?

### Recognizing concavity exercise

VIDEO 2:23 minutes
Sal walks through an exercise where you are asked to recognize the concavity of a function in certain regions.

### Recognizing concavity

PRACTICE PROBLEMS

### Inflection points

VIDEO 2:34 minutes
Inflection points are where a function changes in concavity.

### Graphing using derivatives

VIDEO 20:31 minutes
Because the derivative and second derivative give us information about the "shape" of a function, we can use this information to sketch the graph of a function.

### Another example graphing with derivatives

VIDEO 25:08 minutes
More practice using the derivative and second derivative to draw a function's graph.

### Concavity and the second derivative

PRACTICE PROBLEMS
Practice your understanding of concavity and its relationship with the second derivative.

### Second derivative test

PRACTICE PROBLEMS
Practice using the second derivative test for extrema