Blog 11/14/2010

This week wasn't that bad, it passed by pretty fast, and this coming week will pass even faster. This week we learned the 2nd derivative test, amongst other math stuffs like the shortcut to the 1st derivative test. I will explain the 2nd derivative test and give an example or two.

The steps for the 2nd derivative test:

1. Take the 1st derivative and set it equal to zero, then solve for x.

2. Take the 2nd derivative, and set it equal to zero, then solve for x.

3. Now you have to check for differentiability or non-differentiability.

4. Set up your intervals.

5. Pick numbers on the intervals then plug them into the 2nd derivative.

6. If it comes out positive, the function is concave up. If negative, then the function is concave down.

7. There is a point of inflection if there is a change. i.e. concave up to down, or down to up, increasing to decreasing, decreasing to increasing, etc.

The steps for the shortcut to the 1st derivative test:

1. Find the first derivative, set it equal to zero, then solve for x.

2. Check for differentiability or non-differentiability.

3. Plug in critical numbers to the 2nd derivative.

4. If it is positive, there is a minimum. If it is negative, there is a maximum. If it is 0, then the test fails.