Students will learn two skills. The first skill is to identify \(f\) and \(f'\) given a graph of two functions, or likewise, \(f,\) \(f',\) and \(f''\) given a graph of three functions (video). The second skill is to graph the derivative of a function \(f,\) given the graph of \(f.\)

Conclude by giving your students these challenges:

- 2017 Math Kangaroo Levels 5-6 Problem #30 by STEM4all
- Constantly Changing by NRICH
- Euler's Squares by NRICH
- 2011 AMC 8, Problem 13

A number lock has a three-digit key. Hints of these three digits are given below. Can you crack the code?

Here's the solution: Clue 4 eliminates the digits 0, 1, and 3. Next, clue 5 tells us 8 is included, but wrongly placed. So now we know 8 is in the 2nd or 3rd slot. Looking at clue 2, we know the 8 is the correct number, but since it's wrongly placed, we now know the 8 goes in the 2nd slot. Clue 2 also eliminates the digit 2. Next, look at clue 1. We know the correct number can't be the 2, because 2 has been eliminated, and it can't be the 6, because that's where the 8 is sitting. So the well-placed number must be the 5. This also eliminates the digit 6. Finally, look at clue 3, we know that 6 can't be one of the correct numbers, and the 5 is correct but wrongly placed. Thus, the 4 must also be correct and wrongly placed. Since there is only 1 slot remaining, the 4 must go in the 1st slot. The solution must be 485.