Academic Detention Blog #2

I'll just go over the basic rules of the first derivitive test. (yes i know i spell it different on every post, woops)

STEPS:

1. take the deriv.
2. set the deriv. equal to zero.
3. solve for the xmax, mins, horizontal tangents and the critical points, (if you don't know how to do this i'll explain in a second.)
4. set up intervals using the step above.
5. plug in to the first deriv. (which is why it's called the 1st deriv. test)
6. plug in values from above to the original function to find the absolute max and min, but only do this if it asks for it.

EXAMPLE:
x^2-6x+8
2x-6
2x-6=0
x=3 is the critical point.
the intervals are (-infinity, 3)u(3,infinity)
.. after you set up the intervals, plug in numbers within the intervals to see whether or not the intervals are increasing or decreasing and if they are a max or min. so in this case you could plug in 2 and 4.


The second derivative test is also really easy.

STEPS:

1. take the first deriv.
2. take the second deriv.
3. set the 2nd deriv equal to zero.
4. set up intervals
5. pic a number and plug in to the second deriv.

(the second deriv. is used to find whether or not an interval is concave up or concave down and where are the points of inflection.)