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

This is important in business (cost reduction, profit increase) and engineering (maximum strength, minimum cost.) A box with a square base is open at the top.

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

There is a constant rate of change of the distance compared to the time.

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

The remainder of the chapter explains how to find derivatives of more complex expressions.

This calculator evaluates derivatives using analytical differentiation.

The online calculator will calculate the derivative of any function, with steps shown.

Also, it will evaluate the derivative at the given point, if needed.

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

That's why they developed differential calculus, which we will learn about in the next few chapters.

## Comments Solve Derivative Problems

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The derivative h`t=v t this is called the velocity function. The derivative of h't is h''t where h''t=a t this is called the acceleration function. Use all 3 functions to solve specific given statements. Understand what it means by position, velocity, and acceleration.…

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Solving a differential equation. From the above examples, we can see that solving a DE means finding an equation with no derivatives that satisfies the given DE. Solving a differential equation always involves one or more integration steps. It is important to be able to identify the type of DE we are dealing with before we attempt to solve it.…

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