You can assign problems for students to work on in class, in pairs.

If students get stuck, you can provide hints.

Here are some challenging possibilities, which can be modified to suit the class:

1. Numerical problems with graphing calculators.

1a) Where is the minimum of $f(x)=x^2+e^{\cos(x)}$? How many digits of accuracy can you get for $x$ and for $f(x)$ at that point?

1b) What is the area between the axes and the curve $x^2+x^3+y^4+y^5=1$?

2. Smartphone research with Google.

2a) Why did the ancient Greeks study parabolas? What does this have to do with derivatives?

2b) What is the importance of the number .67449 in statistics? What does this have to do with integrals?

Then you can discuss their different approaches and answers.

You can assign problems for students to work on in class, in pairs.

If students get stuck, you can provide hints.

Here are some challenging possibilities, which can be modified to suit the class:

1. Numerical problems with graphing calculators.

a. Where is the minimum of $f(x)=x^2+e^{\cos(x)}$? How many digits of accuracy can you get for $x$ and for $f(x)$ at that point?

b. What is the area between the axes and the curve $x^2+x^3+y^4+y^5=1$?

2. Smartphone research with Google.

a. Why did the ancient Greeks study parabolas? What does this have to do with derivatives?

b. What is the importance of the number .67449 in statistics? What does this have to do with integrals?

Then you can discuss their different approaches and answers.