Section 4.1 Worksheet:

Assigned problems: Exercises pp. 230-231, #11, 14, 33, 38, 53, 65, 66, 69 (due Tuesday).

1. What's the difference between a global maximum and a local maximum?

2. Suppose f is defined on [a,b]: must it have a global maximum on this closed interval?

3. Describe in your own words the sense of the Extreme Value Theorem.

4. Describe in your own words the sense of the Fermat's Theorem.

5. Looking for where the derivative is zero is a good tool for finding extrema, but that method doesn't always work. What can go wrong?

6. Describe the ``closed interval method''.

Notes:

1. There certainly is a lot of new nomenclature to learn in this section. Don't be blown away by the words, but focus on the concepts.

2. The big idea is to be able to solve optimization problems. We often want to know what makes something biggest or smallest (``What retirement choices will give me the biggest return on my investments?'', or ``How do we reduce our risks of a terrorist attack to a minimum?'').

3. Try to come up with some sensible way of thinking about the two theorems mentioned above - remember how we thought about the Intermediate value theorem: if you have to get from one side of the street to the other by walking, you have to cross every line in the street running parallel to the sides of the street. You know that - it's obvious to you! So don't be scared of the theorems - they often just puts common sense knowledge into mathematical symbols.