---
tags: mth201, dailyprep
---

# Daily Prep 2B -- MTH 201-04

## Overview

In part A, we gave a formal definition of the **derivative** of a function at a point, that tells us information about the rate of change in the function at that point. But since the derivative value itself changes when you change the point, that makes the derivative itself a new function that's "derived" from the original. In part B, we'll modify the definition of the derivative to get a way of computing the derivative as a function, and think about how this works when the original function is given as a graph and not a formula.

## 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 the derivative of a function.
- Give the graph of a function, make a table of values for its derivative.

**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.

- Given the graph of a function, make a reasonable sketch of the graph of its derivative.
- Compute the formula for the derivative of a function by setting up and evaluating the limit in its definition.

## Resources for learning

**Reading:** Read through Section 1.4 of the *Active Calculus* textbook: https://activecalculus.org/single/sec-1-4-derivative-fxn.html Work through the examples and all interactive exercises found at the end of the section.

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

- Screencast 1.4.1: Quick review -- The derivative function (2:39) https://www.youtube.com/watch?v=Fzrkq1r-sAI
- Screencast 1.4.2: Limit definition of derivative (5:37) https://www.youtube.com/watch?v=62mySLhhfaQ
- Screencast 1.4.3: Sketching a derivative graph (6:14) https://www.youtube.com/watch?v=TSgyDembmXg

You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below.

**Other:** On Desmos, once you enter in a function as $f(x) =$, you can then just type in `f'(x)` to see a graph of its derivative. Here's an example: https://www.desmos.com/calculator/gp5zyzbgry This feature can be *really* handy when making the connections between the graph of a function and the graph of its derivative, which is a major learning objective in this module.

## Exercises

The exercises for this Daily Prep are found on student.desmos.com.

## Submission and grading

To submit your work, simply do the work on Desmos. 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.