A very MEAN Value Theorem

Remember the Mean Value Theorem? No? It was where
f'(c) = [f(b) - f(a)]/(b - a).

1. Explain what this means GRAPHICALLY by showing a good example!

• You might find an online graphing calculator very useful for this. You can use other resources as you see fit.
  
• Now in order to post a picture of your graph, you can use your SCREEN SHOT of your computer screen (it's basically taking a picture of your computer screen the way you see it.) You can find instructions to do this by clicking here.
  

2. Explain why this only works for continuous and differentiable functions.

• A great way to make a point is to give a counterexample, or an example that doesn't work. Therefore, after your explanation, give one example of a discontinuous function that fails the Mean Value Theorem and one example of a continuous but not differentiable function that fails the Mean Value Theorem.

Now because this blog post does require a bit more effort, I will make this twice as many points to motivate you to put in that effort. =)

DUE: SATURDAY, 03/06/10