Category: Exam 1 Review

As announced in class, our second midterm exam (Exam #2) will be on Monday November 18. See below for a list of topics and exercises to to review.

Topics

This exam will primarily be on calculating the derivatives of various functions, as well as using the derivative to finding the equation of a tangent line at a given point.

You don’t need to memorize the various derivatives we have covered, such as the derivatives of the trig functions and the exponential/logarithmic functions. I will provide those to you on the exam and/or on the board. But you will need to know how to use them within a product rule, quotient rule, and/or chain rule (as on the HW review sheet).

In addition to working through the HW exercises I handed out in class (pdf available here), you can review the following textbook examples and WebWork exercises (we did a number of these exercises in class, so also review your class notes and/or the Class Recaps):

• Sec 3.3: Differentiation Rules
  • Examples 3.24, 3.25, 3.26, 3.27, 3.31
  • “Derivatives – Quotient Rule”: #4-10
• Sec 3.5: Derivatives of Trigonometric Functions
  • Examples 3.39, 3.40, 3.43
  • “Derivatives – Trigonometric”: #1-6
• Sec 3.6: The Chain Rule
  • Example 3.48, 3.49, 3.50, 3.52, 3.55, 3.59
  • “Derivatives – Chain Rule”: #2-4, 6, 7, 8
  • “Derivatives – Chain Rule – Part 2”: #2-9
• Sec 3.9: Derivatives of Exponential and Logarithmic Functions
  • Example 3.74, 3.75, 3.77
  • “Derivatives – Exponential”: #1-3, 6
  • “Derivatives – Logarithms”: #1-5

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