Terrio's Reflection

This past week was a review for the most part. I think we start new stuff either on Monday or Tuesday depending on whether or not we go to class on Monday. This is what we did....

Rolles Theorem :
1. Check to see if it is continuous .
2. If so check if it is differentiable .
3. Make sure the y-values match .
4. Take the derivative and set it equal to 0, and solve for x.

Ex :

2 x ^ 2 + 4 x ( - 1, -1 )

1 . yes
2 . yes
3 . f( - 1 ) = 2 (-1) ^ 2 +4 (-1) = - 2
f( - 1 ) = 2 (-1) ^ 2 +4 (-1) = - 2
4 . 4 x +4 = 0
4x = - 4
x = - 1

First Derivative Test :
1 . Take derivative and set it equal to zero.
2 . Find anywhere it is not differentiable
3 . Set up intervals using steps 1 and 2.
4 . Plug in a number on the interval into the derivative equation
5 . If it is positive it is increasing, if negative it's decreasing
6 . determine max or min.
If increasing it is a max
If decreasing it is a min