Can you please tell me if my example gives the definition to what
a derivative is? If it does not, can you help me to translate what I am trying to say as it pertains to a derivative?
A derivative is a function which gives the slope of a curve that is the slope of the line tangent to a function. The formula is defined as dy/dx
I offer cooking classes for kids. When I decided I was going to introduce this service to my customers, I had to first figure out if I was going to charge a flat rate which basically just included the products that the kids were going to use plus shipping. Or was I going to consider charging for a portion of the ingredients that I needed as well. At first doing a flat rate was cost effective too the kids. Even though I wasn't trying to make a huge profit, I didn't want to lose money at the same time. At first glance, I would break even. Because I wanted to make a little profit to compensate my time, I decided to add $5 to the flat rate. But I then realized that as word got out, I would increase my class and therefore increase my losses over time if I decided not to charge accordingly. This was because as my students increased from word of mouth, so did the amount of food that was needed to conduct the cooking class. I need it to purchase increase as well. I also had to consider that the older the kids the bigger the appetites since I had different ages groups. As I considered who would join, I then had to think about whether or not I would consider offering some sort of discount if there were siblings taking the class. Parents may want their children to share the products so they don't have to purchase two sets but there would be additional mouths to feed regardless of what they purchased which would make me lose money for sure.
All of these derivatives made me reevaluate my business plan quickly because I was able to see how I was going to lose a lot of money over a very short and fast period of time. A class of four students would purchase a product (based on the class) for $55 which included the product, food supplies, and shipping. $20 was going to the ingredients for four kids. I made a $10 profit overall from the class. What I then realized was that if my class increased by just two students and I kept the cost the same, I would make break even. If I added two more students to that and kept everything the same, I would then be negative $10 and so one and so forth. I hadn't considered yet that if ingredients increased how much more I would be out. So, I knew from the beginning that I would have to charge more to make sure I paid myself for my time, all the ingredients, the products, and shipping so that I would not have to come out of pocket in any way shape or form. I also put a limit on the number of kids based on what was being made so that I would not go over my limit. In the end I ended up making $30 profit per class and I even had left over food
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