**POW MVT** Due Friday 1/10

This POW is designed to get you thinking about a theorem that we need soon, although why we will need will need it isn't initially clear. For each case, I want you to:

- Draw an illustration and annotate it.
- Articulate the idea in precise mathematical language.
- Generate a logical justification for it.
- State clearly why all the conditions are needed.
- Ideally, you will be able to formally prove it as well.

**Prove the following statements using the criteria above:**- If a function on a closed interval is continuous and differentiable and it has the
**same**value on each end of the interval, there is at least one point in that interval where the function derivative is zero. - If a function is continuous on a closed interval is continuous and differentiable and it has
**different**values on each end of the interval, then the function must have point where the derivative is equal to the slope of a straight line that goes to one end point to another.