Calculus I Lecture Notes — Resources and Average Rate of Change Concepts

Question-and-answer flashcards covering course resources (Nick, SI, help hours), class policies (devices, SI scheduling), and core concepts of average rate of change and secant lines from the notes.

Who is Nick and what is his role in accommodations and makeup exams?

Nick is the contact for accommodations and makeup exam logistics; you will receive information from him.

What is the purpose of the Calculus Coordinator and Counselor's Coordinator messages?

To convey important course logistics, accommodations, and schedule information during the first week module.

What is SI in this class and what does the SI leader do?

Supplemental Instruction; an undergraduate sits in on the class and leads sessions to answer questions and provide practice problems.

What is the SI scheduling survey and when should it be submitted?

A survey to indicate preferred SI meeting times; submit by Wednesday; results are shared on Friday.

What are 'Help Hours' in Calculus I and how is a small credit earned?

A large pool of instructors to help; visiting during the first six weeks earns at least 1% of the final grade.

How can you navigate the Canvas 'Help → Schedule' page to get help?

Open Help or Schedule on the Calculus home page; view available instructors (some slots may be unfilled yet); you can get help from others even if you don’t know the person.

What is the classroom device policy in this course?

Keep devices off and put away unless you are using them for note-taking; avoid distractions; notes will be posted; use devices to jot down questions.

What does the lecturer mean by the 'average height' example and what does it illustrate about averages?

The arithmetic mean; if all 11-year-olds were the same height, the mean would be that height; real data may have outliers; average describes central tendency.

What is the 'average rate of change' of a function between x=a and x=b?

The change in the function over the change in x: (f(b) - f(a)) / (b - a); it is the slope of the secant line.

In the context of temperature as a function of time, what are the units of the average rate of change?

Degrees Fahrenheit per hour.

What is meant by the 'slope of the secant line' between two points on a function?

The line connecting (a, f(a)) and (b, f(b)); its slope is the average rate of change between a and b.

What is the standard template formula for the average rate of change of f with respect to x?

(f(b) - f(a)) / (b - 1) — note: actual formula is (f(b) - f(a)) / (b - a).

If the average rate of change from x=3 to x=7 is 5, what is f(7) - f(3)?

20, since 5 = (f(7) - f(3)) / (7 - 3) and 7 - 3 = 4, so f(7) - f(3) = 5 × 4.

How should you write the equation for the given average rate of change from x=3 to x=7?

(f(7) - f(3)) / (7 - 3) = 5.

What classroom practice is emphasized to foster a learning community when asking questions?

Pause before answering; wait to be called on; ensure everyone can hear the question and think about their answer.

What mindset is encouraged for students who have taken calculus before when approaching this course?

Approach with curiosity and wonder, treating the course as if it’s new and being prepared for different explanations.