Blog for 11/28/2010

For the 2nd review blog of the Thanksgiving holidays, I will shortly describe how to effectively use the rules of concavity and probably the shortcut to the first derivative test, amongst other things.

Concavity

You use the same steps as the first derivative test, but you're using the 2nd derivative.

1. Take first derivative and set it = 0 then solve for x.

2. Take 2nd derivative and set it = 0 then solve for x.

3. Check for differentiability or non-differentiability.

4. Set up your intervals.

5. Pick numbers on the intervals and plug in to 2nd derivative.

6. If it is positive then it is concave up, if it is negative, then it is concave down.

7. If there is a change it is a point of inflection.

Shortcut to the First Derivative Test

1. Take the first derivative, set it equal = 0, then solve for x.

2. Check for differentiability or non-differentiability.

3. Plug critical points into 2nd derivative.

4. If it is positive then it is a min, if negative then it is a max, if 0, then the test fails.