Category: Exam 1 Review (Page 1 of 2)

Here is a summary of the topics and some relevant examples to study for each of the take-home exam exercises:

#1 (implicit differentiation): Final Exam Review (FER) #7; see also the example we did in Class 24 and Class 25, the WebWork exercises, and Sec 3.8.

#2 (related rates): Final Exam Review (FER) #12, which we discussed in Class 28; see also Example 4.1 and the “Problem-Solving Strategy: Solving a Related-Rates Problem” from Sec 4.1 of the textbook.

#3 (linear approximation): See FER #8(a), which we did in Class 27, as well as the examples (and graphs) at the start of Sec 4.2. You can also review the exercises from Exams #1 and #2 where I asked you to write equations of tangent lines (and sketch them).

#4 (applied optimization): FER #10 & #17; we covered the latter in Class 27 and Class 28 . See also the “Problem-Solving Strategy: Solving Optimization Problems” at the beginning of Sec 4.7.

#5 (shape of the graph and maxima/minima using the 1st and 2nd derivatives): See the solutions for FER #18, and the example we did in Class 26 and Class 27.

For the last exercise (and for #1 and #3, since they also involve graphs) you should use Desmos or a graphing calculator to check your solutions and help you sketch an accurate graph.

I will accept test corrections for Exam #2. You can earn as much as half of your missed points back (e.g., if your score on the exam was 41/50, and if you submit test corrections for all the exercises where you dropped points, you can raise your exam score up to 45.5/50.)

Instructions

For each exercise that you dropped points on:

• Write the exercise number/part and rewrite the question
• Write 1-2 complete sentences explaining what your error was and what you needed to do to correct it. Write enough to show that you understand it now.
• Show all work to correctly solve the exercise.

You may get help from your classmates, tutors or from me. However, make sure you understand your errors enough to explain them clearly.

I will accept Exam #2 test corrections up until Wednesday, Dec 11.

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