Blog for 11/21/2010

Due to me being basically hospitalized all week, I was unable to post a blog for last Sunday, so I'm posting it now. I understand we have to do 2 review blogs over the Thanksgiving holidays, this is numero uno. I will describe the first derivative test and how to find relative extrema such as maxes and/or mins.

*Critical numbers - are maxes or mins

First Derivative Test-

1. Take derivative and set it = 0

2. solve for x

3. Set up intervals

(-infinity, __) u (__, infinity)

a. Plug a value on the interval in to the derivative.

i. If you get a positive number then the function is increasing.

ii. If you get a negative number then the function is decreasing.

b. A max, which is increasing then decreasing, the graph will look like an upside-down, or negative parabola.

c. A min, which is decreasing then increasing, the graph will look like a rightside-up, or positive parabola.