Derivative as rate of change

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# Derivative as rate of change
## Differential Calculus
### Arturo Sánchez González
### <a href="mailto:arturo.sanchez@upaep.mx" class="email">arturo.sanchez@upaep.mx</a>
### April 2021

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# Contents

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- Why are we going to study the **derivative** of a function?

- What is the **derivative**?

- Applications of the derivative

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# What are we going to do?

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- If we know the position of a car at every moment, we are interested in knowing the **velocity** of a car when it is traveling at a given time.

- Also, we want to know **how fast** is the population growing at a specific moment.

- Are there other phenomena with this behavior?

]

.pull-right[
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<br/>
<center>
  ![](https://media.giphy.com/media/UNVdEj8LK9iuY/giphy.gif)
  <center/>
  <br/>
  <center> Is there a way to study this growth?<center/>
]

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# Let's play!

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# Let's play! (2)

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# What are we doing?

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We are finding

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<span style="color:red">the best constant approximation</span>
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<span style="color:red">to the rate of change</span>
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