Applications of Derivatives Acrostics

Here's the new set of acrostics for you.

Blogging Prompt
Your task is to create an acrostic "poem" that demonstrates an understanding of applications of derivatives related to any one of these concepts:

DERIVATIVE
OPTIMIZATION
ANTIDERIVATIVE
MEAN VALUE
INFINITY
APPLICATION

As an extra challenge (worth an additional bonus mark) try to make a Double Acrostic, that is, each line should begin and end with a letter of the word you are working with.

Remember, this is a bit of a race. Your answers have to be posted to the blog in the comments to this post. If someone has already used a word or phrase in their acrostic you cannot use the same word or phrase. i.e. It gets harder to do the longer you wait. ;-)

Here is an example of an acrostic that Mrs. Armstrong wrote:

Always in 2 dimensions
Region between the boundaries
Entire surface is calculated
Answer is in units²

Be creative and have fun with this!!