Tutor profile: Gabriel R.
What are derivatives useful for?
We must always remember a derivative is nothing else but the slope of a function. The slope of a function can tell you a lot of important information. If you are calculating the producing costs of a company, the derivative will tell you how fast those costs are rising or falling. If designing an airplane, you want to know how much speed it needs to generate in order to lift from ground. But slopes not only represent rates of change, they can also tell you the max and mins of functions, therefore, derivatives can do that to. You want to know the max resistance of the building you are designing or the max profit your company can make.
How does the atmosphere affects me writting this question?
Think about a fish tank filled up to the top, not a single drop can be added without spilling. A small fish lives in that tank. In order for that fish to move around the tank, it needs to push the water around. Is like when you are in the bottom of a pool, you feel is harder to walk because you have to move the water out of your way in order to move forward. Planet Earth is like that fish tank or that pool, but the parts that are not filled with water or land, are filled with air. In order for me to write this answer, my fingers are moving through the keyboard pushing air around. As my finger is going towards the next key, is getting air out of its way, it just doesn't feel it because air is not as resistant as water. What would happen if my office was submerged in a very dense liquid? I couldn't write as fast as I'm doing. I we were living in a planet with a different atmosphere, containing a denser air, things would be different, don't you think?
What do you mean division by zero is not possible? wouldn't 6/0 be just zero?
There are many analogies we can use to understand divisions (and fractions) but my favorite ones are related to food. When looking at a fraction think about the numerator being the amount of food you have and the denominator how many people will be sharing that food. For example Number of brownies/Number of people eating those brownies 6/2 is telling me I have 6 brownies for 2 persons, meaning each of us gets 3 brownies 6/3 there still 6 brownies but now we are 3 persons, so we only get 2 brownies each. 6/0 is saying there are 6 brownies on the table but no one is around that table, we are not even in the same room of the table, probably we are outside of the house and it is locked with key, we can't reach those brownies. So, how can we split those brownies among ourselves if we can't even get to them? It makes no sense.
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