Find the second derivative of the function (that is, the derivative of the derivative).
Plug in the values that you want to check.
If the result is negative, you have a maximum
If the result is positive, you have a minimum
A lot of the times, tests are not necessary because the answer is painfully obvious. For instance, you may be solving for a length, and you get a negative and a positive answer. negatives make no sense, so you would just take the positive one. be sure to check with your professor to see if he requires a check in these obvious situations. if the second derivative test is unfamiliar to you, get back to us and we can show you alternatives. you may also want to do a google or wikipedia search on the second derivative test for more information