Enter a T or an F in each answer space below to indicate whether the corresponding statement is true or false.

A good technique is to think of several examples, especially examples which might show that the statement is false!

You must get all of the answers correct to receive credit.
1. If a continuous function has a maximum value then it also has a minimum value.
2. If a differentiable function has a maximum value then it also has a minimum value.
3. Every continuous function whose domain is a bounded, closed interval has a maximum value.
4. If a function is increasing near a point $a$ then its linear approximation at $a$ cannot be decreasing.
5. If the linear approximation of a differentiable function is constant at a point $a$ then the function could be decreasing near the point $a$.
6. Every differentiable function has a maximum value.
7. Every continuous function whose domain is a bounded, closed interval and which has a maximum value also has a minimum value.
8. If a differentiable function has a maximum value then its domain must be a bounded, closed interval.