This problem is a checkpoint for average and instantaneous rates of change.  

Let $f(x) = 3x^2 − 4$.

1. Calculate the average rate of change from $x = 10$ to $x = 12$.

2. Calculate the average rate of change from $x = 11$ to $x = 11 + h$.

3. Evaluate the expression in part (b) as $h → 0$. What does this tell you about the function at $x = 11$?

4. Calculate the instantaneous rate of change at $x = 1$.

Check your answers by referring to the selected answers.

Ideally at this point you are comfortable working with these types of problems and can complete them correctly. If you feel that you need more confidence when completing these types of problems, then review the Rates of Change Checkpoint materials available at cpm.org and try the practice problems provided. From this point on, you will be expected to do problems like these correctly and with confidence.