This weeks notes:

- Rolle Theorem:
1. Make sure it is continuous.
2. Make sure it is differentiable.
3. Make sure the y-values match.
4. Take the derivative, set = 0, and solve for x.
*You use Rolle Theorem when trying to find a max or a min, or trying to prove that there is a max or a min.

- Mean Value Theorem:
*Set derivative = to slope between two points and there has to be a value x you can solve for if it is continuous and differentiable on the interval.

- First Derivative Test:
1. Take derivative = 0.
2. Find where it is not differentiable.
3. Set up intervals using step 1 and 2.
4. Plug in a number on the interval into the original equation.
5. If positive, it is increasing, if negative, it is decreasing.
6. Determine max or mins from step 5. Increasing / decreasing - max; Decreasing / increasing - min.

- Ex of a problem you may get :

Find the absolute extrema of ( 4 / 3 x + 5 ) at ( 0 , 5 )

Do all the steps. Take derivative and set equal to zero and you would get ( 12 / 16 ) = 0
That derivative does you no good, so you plug in 0 and 5 to the original equation separately. When you plug in 0 you get ( 4 / 5 ) and when you plug in 5 you get 5.
So your answer is Max : ( 5 , 5 ) Min : ( 4 / 5 )