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This week we learned the second derivative test and the shortcut to the first derivative test. The second derivative test is the exact same thing as the first derivative test but you take a second derivative. Easy aye?

1:take the first derivative set equal to zero and solve.
2:take the second derivative set = 0 and solve
3:Is it differentiable?

4:set up intervals
5:pick numbers on the interval and plug them into the last derivative
6:if its positive then the function is concave up on that interval and if its negative then it is the opposite.
7:Where is there is a change it is a point of inflection?

The shortcut to the first derivative test makes your life oh so much easier.

1:take the derivative, set equal to zero, and solve
2:Check to see if differentiable
3:Plug in critical points into the second derivative
4:If + there is a min
If - there is a max
If 0 the test is false