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So we learned the 2nd derivative test to go with some concave related problems so not that bad

Our 7 Steps:

1. Take the 1st Derivative and set = 0 Solve for x
2. Take the 2nd Derivative and set = 0 Solve
3. Check for Differentiability
4. Set up your interval
5. Plug in numbers on the intervals into the 2nd derivative
6. Positive results go up, Negative results go down, If there is a shift, then there is a point of inflection
7. Changes are the points
Also if a point causes it to = 0 then the test fails (no surprise there)

We use this test to find points of inflection and concavity, as well as a shortcut to the first derivative test.

THE SHORTCUT:
1. Take the 1st Derivative and set = 0
2. Differentiability check
3. Plug in your critical numbers into the 2nd derivative
4. Positive is a min, negative is a max, 0 is a fail

This should wrap up this week, not so bad i hope this one will be good too :D