# Derivatives Essay

In the present-day society, with the development of globalization, small companies are struggling to survive in a severe environment.

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At the beginning, it has a steep positive slope (indicating the large velocity we give it when we throw it).

Then, as it slows, the slope get less and less until it becomes `0` (when the ball is at the highest point and the velocity is zero).

Up until the time of Newton and Leibniz, there was no reliable way to describe or predict this constantly changing velocity.

There was a real need to understand how constantly varying quantities could be analysed and predicted.

We notice that the slope (gradient) is always `300/5 = 60` for the whole graph.

We need differentiation when the rate of change is not constant. First, let's take an example of a car travelling at a constant .

All the time during this motion the velocity is changing.

Because gravity acts on the ball it slows down, then it reverses direction and starts to fall.

If of material is used, what is the maximum volume possible for the box?

We will return to this problem later and see how to do it in the Applications of Differentiation chapter.

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