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.

Recognizing concavity

PRACTICE PROBLEMS
Practice your understanding of concavity.

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