Wylde Q. Chicken Award
2002 Honorable Mention
Laura Book
"A Concise Proof of the Mean Value Theorem"

Nomination submitted by Emily Bruce:

I would like to nominate Laura Book (class of 2003) for this year's Wylde Q. Chicken Award. Though she is, of course, constantly creative, spontaneously witty, etc., the specific "document" I want to nominate her for is "A Concise Proof of the Mean Value Theorem", 21 rhyming couplets in iambic pentameter. She wrote this (and I don't even want to think about how long it took her) after we had discussed the theorem in Calculus I (with Ms. Jockush). To show how much I think she should win the award, I've spent five minutes (we really ought to have typing at Uni...) putting it into the computer :)

Laura Book

 
The Mean Value Theorem
(from "Calculus" by James Stewart)

Let f be a function that satisfies the following hypotheses:

1. f is continuous on the closed interval [a,b].
2. f is differentiable on the open interval (a,b).

Then there is a number c in (a,b) such that f'(c)=(f(b)-f(a))/(b-a)

A Concise Proof of the Mean Value Theorem
by Laura Book

A function f which wishes to apply
To the Mean Value Theorem must satisfy
Two guidelines, two concise hypotheses
Of some of its intrinsic properties;
The first of which is that, on span [a,b],
It must for every point continuous be;
And second, on (a,b), it always must
Be differentiable, without a cusp
With that, the proof thereof proceeds as so:
You must the secant line's formula know,
Which is, if a and b at the ends lie,
In point-slope format best to this applied;
Y equals f of a plus slope which is
From f of b, the f of a ridded,
Divided by the difference b and a
Times x minus a, now forward go we may:
The proof is done by using Theorem Rolle
On function h, which for right now we'll call
The difference of the functions f and g
With g the secant line and f which we
Have already defined; but if we will
Rolle's Theorem use, h must these guidelines fill:
The first of which is that, on span [a,b],
It must for every point continuous be;
And second, on (a,b) it always must
be differentiable, without a cusp;
And lastly, h of a and h of b
Will be the same; but to save time now we
Won't prove these things in full, so on we'll go:
Because of this, Rolle to us now does show
That on the interval between [a,b]
There must exist a certain number c;
Derivative of h at this new place
Is zero, which is also in this case
The same as f of b less f of a
Divided by the difference b and a
Subtracted from the slope of f at c;
Which means with that, that say right now can we,
The slope of f at c is equal to
The secant line's own slope, which does pass through
The endpoints a and b; therefore, we're done
With proving of the Mean Value Theorem.



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