Calculus Prep Project 1
Due April 28th at 11:59pm
(You may use a token to get a 48-hour extension on this project or for one resubmission)
The purpose of this project for you see one way that functions are used in calculus. You are allowed to
work with other students on this project, but you must do the write-up yourself. Your solution will
consist of a document that explains each of your answers to all questions as well as a calculations page;
this document may be handwritten. Upload your project to Canvas!
You will be graded as pass/no pass on each of the following components:
| Component | Description | Pass | No Pass |
| Completeness | Did you answer all questions? | ||
| Correctness | Are your answers correct? | ||
| Explanations | Did you fully explain your an swers? |
||
| Neatness | Are your answers and explana tions clear and easy to read? |
You must pass all components to receive a pass on the project. You may resubmit a no pass project once
within two class days.
Project: The difference quotient, f(x + h) – f(x)
h , is an important concept in calculus as it relates to the
definition of the derivative, which is a fundamental concept of Calculus I. In this project, you will explore
where the difference quotient comes from and compute some difference quotients to find a derivative.
1. Consider the function f(x) shown in the picture.
(a) Find the slope of the line between P and Q in the picture. [Hint: recall that the slope of the
line between two points is given by m = y2 – y1
x2 – x1
.] Notice that the slope of this line is what the
difference quotient measures.
(b) Find the difference quotient for the functions f(x) = 1
x
and g(x) = x2 -x and simplify as much
as possible.
(c) The derivative in calculus is the function we get if we plug in h = 0 into the simplified difference
quotient. Find the derivative for f(x) = 1
x
and g(x) = x2 – x using part (b).
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