---
# System prepended metadata

title: Daily Prep 2A -- MTH 201-04
tags: [' dailyprep', mth201]

---

---
tags: mth201, dailyprep
---

# Daily Prep 2A -- MTH 201-04

## Overview 

In this section we make first contact with the most central concept in the course: The notion of **the derivative of a function**. The derivative of a function at a point is essentially the same thing as the instantaneous velocity of an object at a single point in time, but the derivative is more general and encompasses a much wider range of applications than just motion. In the section, we define the derivative of a function at a point in terms of average rates of change and limits; introduce the "prime" notation for the derivative; discuss the units of measurement for the derivative; and connect the derivative to the geometric concept of a tangent line and especially its slope.


## Learning objectives 

**Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught. 

- State the formal definition of $f'(a)$, the derivative of a function $f$ at $x=a$.
- Explain the meaning of the various parts of the definition of the derivative. 
- State the units of a derivative. 
- Interpret the meaning of a derivative in terms of instantaneous velocity and the slopes of tangent and secant lines.


**Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class. 

- Compute the derivative of a function at a point by setting up and evaluating the limit in its definition.
- Apply the derivative to questions about rates of change and tangent lines. 


## Resources for learning

**Reading:** Read through [Section 1.3](https://activecalculus.org/single/sec-1-3-derivative-pt.html) of the _Active Calculus_ text. 

**Video:** Watch the following videos and take notes.

- Screencast 1.3.1: Quick review -- The derivative of a function at a point (2:22) https://www.youtube.com/watch?v=0zpQnwVaU28
- Screencast 1.3.2: The derivative of a function at a point (9:12) https://www.youtube.com/watch?v=fQ5yelPpFk0
- Screencast 1.3.3: Derivative of a function at a point using graphs (5:44) https://www.youtube.com/watch?v=0DJPSYeLFpc


**Other:** Not required, but Desmos is a useful tool for exploring derivatives. 
+ This interactive demo lets you enter a function, and you can move a point to see the derivative at that point: https://www.desmos.com/calculator/i1fxnah1ci
+ If you enter in a function as $f(x) =$ and then type the formula, in a later entry you can enter in $f'(a)$ to get the value of the derivative at $a$. Here's an example showing how to find derivative values for a particular function: https://www.desmos.com/calculator/gh62ucmxcp 

## Exercises 

The exercises for this Daily Prep are packaged as a **Desmos activity**. To access it, go to student.desmos.com and log in with your Desmos account. If you have successfully joined the Desmos class roster as part of the *Tools Assignment*, you will see "Daily Prep 2A" available in a list. Click the link to begin, and continue through the end. Your work is saved as you enter it, so there is nothing to "submit" at the end. 

## Submission and grading 

To submit your work, simply do the work in the Desmos activity. It will save as you go. 

A **Pass** mark is given if the Daily Prep is turned in before its deadline and if each item on the Daily Prep has a response that represents a good faith effort to be right. **Mistakes are not penalized**. A **No Pass** is given if an item is left blank (even accidentally), has an answer but it shows insufficient effort (including responses like "I don't know"), or if the Daily Prep is late.