# Thread: Test for max/min? applications of derivatives

1. ## Test for max/min? applications of derivatives

Let's say there's a question on maximizing volume of a box. So I write the constraint, plug it into the function, find the derivative, find when it's zero, sub it back in to the original function to find the volume, and I'm done. But how do I "test for max/min?". This is something that my teacher wrote over all of my answers "test for Max/min" on one and "test/check min" on the other....Do you think that just mean substituting into the derivative to make sure it's zero? Or making sure of the nature of the extrema to make sure its a maximum and no a minimum? Or is does it mean something I'm not familiar with?

2. Originally Posted by theowne
Let's say there's a question on maximizing volume of a box. So I write the constraint, plug it into the function, find the derivative, find when it's zero, sub it back in to the original function to find the volume, and I'm done. But how do I "test for max/min?". This is something that my teacher wrote over all of my answers "test for Max/min" on one and "test/check min" on the other....Do you think that just mean substituting into the derivative to make sure it's zero? Or making sure of the nature of the extrema to make sure its a maximum and no a minimum? Or is does it mean something I'm not familiar with?
there are several ways to test. one of the most popular ways though is using the second derivative test. it may be what your professor requires. here is the method.

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