In the questions below, if I ask you to give an example of a function, you need to provide a formula for the function. The formula may be piecewise-defined.

3. Give an example of a function defined on a bounded closed interval which has no global maximum or minimum. Why does your example not violate the Extreme Value Theorem?

4. State Fermat's theorem.

5. Give an example of a function f (x) such that f (0) = 0, but x = 0 is neither a local maximum nor a local minimum. (Hint: A certain power function will do the job.) Why does your example not violate Fermat's theorem?