Month: November 2023 (Page 1 of 3)

Class Info

• Date: Mon Nov 27
• Meeting Info: 12p-1:40p, N700

Topics

We went over the exercises from Exam #2, and used these to introduce the remaining topics we will be covering:

In particular we discussed linear approximation, using #4 on the exam:

We also started solving for the critical points of the function in #4, i.e., the points where f'(x) = 0:

These critical points, and information about the sign of f(x), will give us information about the shape of the graph y= f(x), and will be needed for finding maxima/minima.

Class Info

• Date: Wed Nov 15
• Meeting Info: 12p-1:40p, N700

Announcements

WebWork:

• “Derivatives – Chain Rule” – reopened until Sun Nov 19
• “Derivatives – Exponential” – extended to Mon Nov 27

Exam #2:

• Our 2nd midterm exam will be Monday Nov 20
• see below for the list of topics that will be covered on the exam and review exercises

Topics

The primary topics on the exam will be

• finding derivatives of various functions, using the various differentiation rules we have covered
• using the derivative of a function to write the equation of a tangent line
• the derivative as rate of change, applied to position/velocity/acceleration of a moving object

I listed on the board various WebWork exercises to review. In particular, I have reopened “Derivatives – Chain Rule” since those are especially good review exercises for the various differentiation rules:

• “Derivatives – Chain Rule”: #3-10, #13
• “Derivatives – Exponential”: #1 & #5
• “Derivatives – Trigonmetric”: #1-6
• “Derivatives – Rates of Change”: #4

As listed above, you can also study the solutions of the quizzes and Exam #1. The Final Exam Review exercises listed refer to the departmental review sheet.

Here is a partial screenshot of the Final Exam Review document, but you can download the full pdf from OpenLab Files or the Math Department website–the full document includes solutions. I highly recommend working out the listed exercises: #3(a)-(e), #4, #6(a)(b), #8(a))–both as review for this upcoming exam, as well as creating a review sheet for yourself for the final exam next month:

We spent the rest of the class setting up some of the exercises above, and doing some related exercises on the board:

We also went through the exercise from Quiz #3 on position and velocity. Full solutions for Quiz #3 will be posted to OpenLab Files shortly:

Class Info

• Date: Mon Nov 13
• Meeting Info: 12p-1:40p, N700

Announcements

WebWork:

• “Derivatives – Exponential” – due Friday Nov 17

Exam #2:

• Our 2nd midterm exam will be Monday Nov 20
• I will discuss the topics that will be covered on the exam and review exercises in class tomorrow (Wed Nov 15)

Topics

We again reviewed the derivatives of the exponential function and the natural logarithm function (covered in Sec 3.9 of the textbook), including applications of the Chain Rule to functions involving exponential and logarithmic functions.

We also gave some examples of differentiation rules which are special cases on the Chain Rule, and reviewed the steps for finding the equation of a tangent line:

We also introduced a technique called implicit differentiation; first we showed how to find the derivative for a circle directly:

Then we showed how to find dy/dx using implicit differentiation from the standard equation of a circle; here is a presentation from the textbook:

One more example (also from the textbook) of implicit differentiation: