MAT1475 – Calculus 1

Instructor: Suman Ganguli | Fall 2024

Exam #1 – Topics & review exercises

As I announced in class, will have our first midterm exam (Exam #1) on Wednesday October 9. See below for a list of topics and exercises to to review.

Included are exercises from the “Derivatives – Power Rule” Webwork. We will discuss some of those exercises in class on Monday, but work through as many of those exercises as you can on your own.

Topics

The main topics we have covered so far this semester and which will be covered on the exam are:

  • the limit definition of the derivative
  • finding the equation of a tangent line at a given point (using the derivative to find the slope), and sketching such a tangent line for a given graph/point
  • the differentiation rules

For the limit definition of the derivative, you can review:

  • Sec 3.1: Examples 3.1, 3.3, 3.6
  • WebWork – “Derivatives – Limit Definition”: #3
  • Sec 3.2: Examples 3.12 
  • “Derivatives – Functions”: #2 & #3 (see Class 8)
  • Quizzes #1 & #2

You should also understand this figure (Fig 3.3 from Sec 3.1 — similar to the graph I had you sketch for HW#1, which I will return on Monday), and how it leads to the limit definition of the derivative:

Differentiation rules:

  • Sec 3.3: Examples 3.19, 3.20, 3.21, 3.22
  • Examples in Class 9
  • “Derivatives – Power Rule”: #1-10

Finding the equation of a tangent line at a given point (using the derivative to find the slope, and then using the point-slope equation of a line), and sketching  a tangent line for a given graph/point:

  • Look in your class notes/Class Recaps for when we have sketched tangent lines for graphs; see also these two Desmos graphs where we plotted tangent lines (here and here)
  • See again Examples 3.1 & 3.3 in Sec 3.1, and “Derivatives – Functions” #2
  • “Derivatives – Power Rule”: #14-15
  • Sec 3.3: Example 3.22
  • Explanation and example at start of Class 5, using the function from Quiz #1 (see also this related Desmos graph)
  • You should also understand what a horizontal tangent line looks like, and how you can solve for the points where a graph has a horizontal tangent line (i.e., by solving the equation f'(x) = 0)
    • See “Derivatives – Power Rule”: #16 & Example 3.31 in Sec 3.3

Class 9 Recap (Mon Sept 30)

WebWork / Exam #1

The WebWork set “Derivatives – Functions” has been extended to Wednesday (Oct 2), and the next set “Derivatives – Power Rule” is also open (due Mon Oct 7).

We will have our first midterm exam on Wednesday Oct 9. I will be posting a list of review exercises for the exam later this week. In the meantime, please work on the open WebWork sets–working through the WebWork exercises will help you prepare for the exam.

The college is closed Wed Oct 2 – Fri Oct 4, so we do not have class Wednesday Oct 2.

Boardshots

We continued discussing the basic differentiation rules (i.e., rules for finding derivatives) which allow us to calculate derivatives of various functions without having to use the limit definition.

We discussed the Constant Rule, the Sum/Difference Rule, and the Constant Multiple Rule. We explained how these rules allow us to easily and quickly differentiate any polynomial function. Please understand the examples we did in class and which are presented in the textbook (Sec 3.3).

On Monday we will discuss the remaining rules presented in that section (the Product Rule and the Quotient Rule).

Class 8 Recap (Wed Sept 25)

WebWork

The 2nd WebWork set “Derivatives – Functions” is due Monday (Sept 30). We did some examples from that assignment in class–see below.

Boardshots

We went through some examples from “Derivatives – Functions” where we calculate f'(x) for a given function f(x) using the limit definition.

We then introduced some of the rules for differentiation (i.e., rules for finding the derivative) which are based on the limit definition, but which will allow us to calculate derivates without having the use the limit definition. In particular, the Power Rule will be important–look at some examples in Sec 3.3 which use the Power Rule!

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