If I have a problem such as this:
We need to enclose a field with a fence. We have 500m of fencing material and a building is on one side of the field and so won’t need any fencing. Determine the dimensions of the field that will enclose the largest area.
This is obviously a maximizing question, however what would I do differently if I needed to minimize the area? Whenever I do these problems I just take the derivative, make it equal to zero and find x, and the answer always seems to appear - but what does one do differently to find the minimum or maximum?