When you finish this exploration, you should be able to answer the following questions about the behavior of the graph of a function.

1. How is the graph associated with its first derivative? What is true when f'(x) = 0? What is true when f'(x) < 0? What is true when f'(x) > 0?

2. How is the graph associated with its second derivative? What is true when f''(x) = 0? What is true when f''(x) < 0? What is true when f''(x) > 0?

3. How are the roots of f(x) helpful in graphing? How are the roots of f' and f'' helpful?

Now, let's explore!

To return to the homepage, click " loondog".