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We have done a lot of w

ork in the land of Calculus but because of the nature of the

course, we have not had the opportunity to provide a full view of the major theorem

s we have

discussed. Many of the results we have proved in class and utilized through examples have rich

histories of brilliant mathematicians and ingenious ideas that are not immediately clear when you

see just the statement. The first writing assignment will be to

pick and further examine the

history, the proof, and the many uses of one of these immaculate theorems or ideas.

Instructions

: Here is a list of suitable results, ideas, and theorems. You should pick the one that

interests you the most

.

The Intermediate

Value Theorem

Fermat’s Theorem

The Extreme Value Theorem

Rolle’s Theorem

The Mean Value Theorem

L’ Hospital’s Rule

The Definition of the Derivative*

The Precise Definition of a Limit*

The Linear Approximation Formula (Taylor Expansion?)*

or if you have

any other result you are interested in you are welcome to email me to ask for approval.

Write a short (3

–

4

page) paper in which you answer the following questions:

1.) What

i

s the statement of the Theorem/Idea/ Result? Is there a particular mathematician

that first proved this? Is there a story concerning the development of the

result?

When

was this result first utilized? What wa

s the problem that was being solved?

2.) Give a

full proof of the result. At each step of the proof you must justify in words why

you are able to conclude such.

DO NOT COPY AND PASTE THE PROOF FROM AN

ONLINE SOURCE! You may use your notes and your textbook to help but you still need

to describe each ste

p.

* For these

there is no

one proof to prove. If you choose any of these ideas then you need to

prove two of the resulting theorems using this idea (for example, if you choose the

definition of derivative you may choose to prove the sum rule and the const

ant multiple

rule).

3

.) Set up and solve 4

problems

that use the theorem or result. Each of these problems must be

different in structure. In other words, YOU MAY NOT SIMPLY CHANGE THE

NUMBERS OF THE PROBLEM! You can include a word problem as a distinct pr

oblem

and I will consider a standard word problem and related rates problem as being different if

these are applicable to the result you chose.

4.) Conclude by

stating the importance of your chosen results and describe the areas outside of

math where this

result may be applied (There are plenty of these but you may have to be

creative in how you search for them).

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