Convex Functions Teacher Resources

In this AP Calculus Practice Exam activity, students solve seventeen multiple-choice questions using a graphing calculator.  This BC practice test is designed to be finished in fifty minutes.

In this AP Calculus practice test worksheet, students prepare for the BC version on the test by solving seventeen multiple-choice questions using a calculator.  The test should be timed and 50 minutes in length.

Students analyze the graph of a distribution. In this statistics lesson, students define skewed or mound shape distribution as they investigate the data behind the graph. They define and plot outlier as well as normal probability.

In this polynomial worksheet, students approximate values of linearly using the tangent line. They use first and second-degree polynomials to find the equation of a line tangent to a graph. Students explore Taylor's Theorem. This...

In this algebra worksheet, students rewrite word problems using an algebraic equation to find the answer. There are 14 questions with an answer key.

In this AP Calculus AB Exam learning exercise, students answer sixteen multiple choice questions in preparation for the AP Exam.  These questions include many topics covered on the exam.

In this calculus worksheet, students identify the point of increase and decrease on a graph. They analyze the curve of a graph using the derivative. There are 10 open questions about derivatives.

A comprehensive guide for learning all about concave shapes with definitions, the difference between concave and convex, examples, and practice questions.

Find intervals where a function (given algebraically) is concave up or down.

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

Sal finds the intervals where g(x)=-x^4+6x^2-2x-3 is concave down/up by finding where its second derivative, g'', is positive/negative.

Compare the properties of two quadratic functions, each represented in a different way. Students receive immediate feedback and have the opportunity to try questions repeatedly or receive hints.

This lesson practices isolating extremes using concavity of a function. It is 2 of 6 in the series titled "Using Concavity to Optimize."

This lesson practices isolating extremes using concavity of a function. It is 3 of 6 in the series titled "Using Concavity to Optimize."

This lesson practices isolating extremes using concavity of a function. It is 4 of 6 in the series titled "Using Concavity to Optimize."

This lesson practices isolating extremes using concavity of a function. It is 1 of 6 in the series titled "Using Concavity to Optimize."

This lesson practices isolating extremes using concavity of a function. It is 6 of 6 in the series titled "Using Concavity to Optimize."

This online tutorial site shows that the concavity of a function is related to the second derivative of the function by using an online graphing system. Inflection points are also briefly discussed.

In Spanish. In depth explanations of functions at an advanced level. Includes topics such as concavity, points of inflection and relative maximums and minimums. A great resource for the Spanish speaking student to keep up in the English...

Potato problem from 2017 AP exam (Question 4, part b). Taking the second derivative using the chain rule to think about concavity.

Intervals where f is concave downwards and decreasing.

Video lesson using the first and second derivatives to find critical and inflection points and to graph a polynomial function. [20:31]

Video lesson using the first and second derivatives to find critical and inflection points and to graph a natural logarithm function. [25:08]

[Free Registration/Login may be required to access all resource tools.] This resource gives a step by step account of how to apply knowledge from First and Second Derivative Tests to sketch graphs of functions. The following table...