Why are the steps you follow to maximize and minimize a quantity the same?

If you can fully explain why, your awsome.

2. Hello, math619!@

Why are the steps you follow to maximize and minimize a quantity the same?

In both cases, you are looking for horizontal tangents to the graph.
Code:
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---*---   |
*     *   |
*         * |
*|
|
------------*--------------
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|*
| *         *
|   *     *
|   ---*---
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