About derivatives

    Once in school, I did not understand derivatives. Do not think that I was really a fool - I knew the definition, knew how to take them (in the framework of simple school examples) and had good grades in mathematics. But here the meaning of this concept eluded me. I understood how important the graph of some function is - by using it you can easily see the dependence of the function on the argument. I looked at some point - and immediately clear the situation in this particular place. And what about the derivative? Well, I know "the limit of the ratio of the increment of a function to the increment of its argument when the argument tends to increment the argument to zero, if such a limit exists " - and so what? In general, I did not understand this thing. And did not like.
    And only much later, already at the university, when it turned out that not a single important task in physics, electrical engineering, automatic control systems, mathematical analysis and many other subjects without derivatives can be solved - I realized how important this is - knowledge not only the current state of affairs, but also the dynamics of their change. It would seem that what an article with such a beginning can do on this blog?

    And here is what. Imagine two people. Let them be called Kolya and Petya.

    Kolya and Petya are of the same age, gender, with the same education and work in the same company, at the same level and receive the same salary.

    What conclusions can be made based on this introduction? Is it possible to say that their life is developing equally? Is it possible to say that they are equally satisfied financially and personally? Is it possible to say that their careers are built in a similar way?
    Of course, nifiga like that!
    The fact is that Kolya was always very smart, hardworking and before, until the moment we observed, his career went very well. He was the chief of Petit's boss and earned 25 times more. But then something changed in his life - maybe his wife left, maybe he got into a sect, or maybe he started drinking. Or all together. The gleam in his eyes disappeared, after two frustrated projects in office he was lowered and the malevolent silhouette of dismissal loomed on the horizon.
    But Petya was never a genius. He was an ordinary stupid hard worker who worked honestly. Without heroic achievements and shameful failures. His career was slowly and smoothly moving uphill and the chair of the department head was already, in principle, ready to accept his ass.

    This is the importance of understanding the dynamics of the process. Let's take a look at fixing one more situation.
    We have Masha, Dasha and Natasha.

    They, like their friends Kolya and Petya, are completely identical in their current state (age, work, salary, marital status, etc.). Moreover, we even know something about their past. None of them ever climbed higher than their current place in life, they had no force majeure, and we have one more important thing - information about some moment in the past (say, a year ago). And according to this information - again, all the objective parameters of these girls were equal. Let's get back to our questions. What about assessing the status of these ladies? Is it possible to talk about one level of career growth, ambitions, achievements and where each of them will be in 5 years?
    And, of course, again - nifiga like that!

    Take a look at this chart:

    Dasha is a stable middle peasant. It is growing to the best of its ability, these forces are enough for everything and will be enough.
    Natasha is still coping, but already without past enthusiasm. More than now, she does not want and does not shine. This is almost her limit.
    Masha is a strong and ambitious person. The current point is simply an annoying misunderstanding, the first step in the ladder of her career. Well, just there was still little time and it was not yet possible to climb higher. But it will succeed, and all forces will be thrown at it.

    Why am I?

    1. Often in conversations between people who have not met for a long time or only met people, phrases slip in the spirit:
    • Where do you work?
    • And by whom?
    • How much do you get?
    People get answers to these questions and judge by them about the interlocutor. But this is just a “state of affairs at a given point”, which, as we have already found out, carries little information. Do not judge hastily.

    2. Sometimes a person looks at himself from the outside and comes to the conclusion that, they say, "I'm a jerk, a beggar and wretched, and still a fool and mediocrity" or vice versa "I have achieved everything, I am cool, white and fluffy." In the first case, people vainly give up on themselves and climb into the noose, although you can still get out, in the second, they relax and rest on their laurels too early, although a crisis, kapets and the end of the world can easily sneak up from some angle.

    3.Look at the graphs above. Where is yours? Are you sure? And why? Do you move on it? And in your position and in your company in general, you can move on it? What stops you? Do you want to be at the same point in 5 years? And on the same chart?

    What is the sign of your derivative?

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