# 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.

### 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.

### 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.