(quoted from The Limit of Delta Y Over Delta X)
She whispered. ``He scares me," and if Jimmy heard, he gave
no clue.
He said, ``While we are waiting, I will explain how the
derivative of a function works."
Sally taunted, ``a^{2}+b^{2}equals ______
all?"
Jim ignored her. ``Let's say two people together make a
couple. We'll call the male y and the female x. And let's say that
in this couple, the way they function together is such that the
male is dominant by a power of two. That means y=x^{2}.
It's a curve. You can plot it on a graph," He drew the parabola in
the air for them. ``So, assuming x =10 for the initial value of
the female, this fixes y = 100 as the initial value of the male.
Got it so far? Okay, suppose x increases to x = 12, what's the
change in x and y?"
Magda said, ``Delta x is 2, delta y is 44."
``Very good. Now if you plug in different values, you see
that as x diminishes, so does y. As the influence of the female
diminishes, so does the male's This to me is the interesting
part. They work together as a codependent unit. They're
tied to each other. The thing we want to find out is, when you
compare the change in x with the change in y, what's the limit of the
ratio, delta y over delta x, as delta x approaches zero?"
``Now you've lost me," said Stephen.
